Last day at work before our break for Christmas week!
And I finally managed to finish Jake's MET/Waddington model problem. Now that the Maple program is done and sent in, the ball is now officially in his court...I have nothing to do until he gets back to me (hopefully not with news that I horribly bungled the analysis).
Friday, December 22, 2006
Wednesday, December 20, 2006
Competence test!
It turns out that installing the GeForce Go 6800 should actually be pretty simple, since Dell designed the 9300's to handle the extra heat that these produce. It's the 6800 Ultra that requires a new heatsink and some other stuff. So I should be able to do this myself. This is good...should save me $30 or $40 and a trip to Best Buy (never fun during the holidays...). I looked up the instructions to replacing your video card on Dell's website, and it's actually pretty straightforward.
Penny foolish
So, I just spent $340 on a new nVidia GeForce Go 6800 (256 meg VRAM) video card for my laptop. I really wanted a new video card, but I mean...jeez. $340. Can't believe I just spent that much!
Well, I justify it to myself as, The computer is my gaming console. I'm buying this crazy new video card in lieu of getting a next-gen console, which would be just as expensive, all things considered. Also, this card will cost an additional 30 or 40 dollars installed, because I'm not going to risk royally screwing up my laptop by trying to do it myself. Sigh. I never thought I'd sink so low as to pay the Geek Squad to do something for me, but here I am...
Anyway, this is good, I think, in the long run. With 1.2 gigs of RAM and this new video card, I should be set as far as games go for a while yet. My centrino processor has an equivalent speed of about 2.5 GHz, so that's still pretty decent.
But...I mean, damn. $340.
Well, I justify it to myself as, The computer is my gaming console. I'm buying this crazy new video card in lieu of getting a next-gen console, which would be just as expensive, all things considered. Also, this card will cost an additional 30 or 40 dollars installed, because I'm not going to risk royally screwing up my laptop by trying to do it myself. Sigh. I never thought I'd sink so low as to pay the Geek Squad to do something for me, but here I am...
Anyway, this is good, I think, in the long run. With 1.2 gigs of RAM and this new video card, I should be set as far as games go for a while yet. My centrino processor has an equivalent speed of about 2.5 GHz, so that's still pretty decent.
But...I mean, damn. $340.
Tuesday, December 19, 2006
Pointless worrying
So, I can't seem to stop wondering about grad school.
On the one hand, and what I say to anyone who asks, is that I'd be perfectly happy to go to any of the 8 schools I applied to, and that I really just hope I get in somewhere. This is basically true, although there's no question that I do have preferences within my 'I'd be happy...' range.
Geography is a pretty big thing to me. I didn't apply to any schools in the Southeast or the Midwest, because I don't think I'd want to live in either area, and only applied to 2 in New England...the rest are all out West. I applied to 1 school in San Diego, 1 in Santa Barbara (near LA), 2 in the Bay Area, 1 in Phoenix, and 1 in Seattle. Of these places, I think I'd like San Francisco or Santa Barbara the best. 60-70 degrees all the time sounds just about perfect for me...
However, there's also the fact that the best schools I applied to are (roughly in order of preference) Stanford, Harvard, and MIT. Unquestionably, if I get into Stanford, that's going to be my pick. (Unless something seriously unexpected surfaces in the interview process, natch.) Harvard and MIT, though, are both in Massachusetts...and while they are both wonderful schools, do I really want to live in New England? It's frickin cold up there!
UCSF and U Washington are probably next down the list in terms of the education, with UCSD, UCSB, and finally ASU bringing up the rear. The real question, I guess, is what I'd do if I got rejected from Stanford, but accepted into either Harvard or MIT and also, say, UCSF. That would be a pretty distressing choice... I guess I'd have to base my decision on the interview process.
Honestly, though, like I said before...just so long as I get in somewhere. I really don't know what I'd do if I didn't get in somewhere for next year. I guess I'd either have to do a master's degree here at UGA (not sure whether I'd do physics or genetics, though), which would be okay, although I really don't want to spend more time in Athens, or, alternately, I could just go to San Francisco or San Diego and try to attach myself to the school in some way. Maybe I could get a job as a lab technician or something, or just volunteer in someone's lab, while working full-time elsewhere, and hope they accept me for the following year. Hopefully it will not come to that!
On an unrelated note, I feel pretty shitty today. Just a head cold, I guess, but it's still pretty unpleasant. At least work is predictably stress-free this week. I think spending time at my parents freezing house tends to batter my immune system pretty hard. I wish they'd see the value of heating! (I mean, sure, it costs money...but being cold all the time messes with your health.)
I need to get cracking on my research project. I told Jake I'd have it done by the end of the break, and the break isn't all that long. I managed to leave my notes from our last meeting at home today, though, and I'm not really able to do much here without those, so I guess I'll really wade into it tomorrow. I'm not working tomorrow...I'm not really doing anything tomorrow, come to think of it, so I suppose it would be a good opportunity for me to settle down at Jittery Joes with my laptop and try to crank through this stuff.
On the one hand, and what I say to anyone who asks, is that I'd be perfectly happy to go to any of the 8 schools I applied to, and that I really just hope I get in somewhere. This is basically true, although there's no question that I do have preferences within my 'I'd be happy...' range.
Geography is a pretty big thing to me. I didn't apply to any schools in the Southeast or the Midwest, because I don't think I'd want to live in either area, and only applied to 2 in New England...the rest are all out West. I applied to 1 school in San Diego, 1 in Santa Barbara (near LA), 2 in the Bay Area, 1 in Phoenix, and 1 in Seattle. Of these places, I think I'd like San Francisco or Santa Barbara the best. 60-70 degrees all the time sounds just about perfect for me...
However, there's also the fact that the best schools I applied to are (roughly in order of preference) Stanford, Harvard, and MIT. Unquestionably, if I get into Stanford, that's going to be my pick. (Unless something seriously unexpected surfaces in the interview process, natch.) Harvard and MIT, though, are both in Massachusetts...and while they are both wonderful schools, do I really want to live in New England? It's frickin cold up there!
UCSF and U Washington are probably next down the list in terms of the education, with UCSD, UCSB, and finally ASU bringing up the rear. The real question, I guess, is what I'd do if I got rejected from Stanford, but accepted into either Harvard or MIT and also, say, UCSF. That would be a pretty distressing choice... I guess I'd have to base my decision on the interview process.
Honestly, though, like I said before...just so long as I get in somewhere. I really don't know what I'd do if I didn't get in somewhere for next year. I guess I'd either have to do a master's degree here at UGA (not sure whether I'd do physics or genetics, though), which would be okay, although I really don't want to spend more time in Athens, or, alternately, I could just go to San Francisco or San Diego and try to attach myself to the school in some way. Maybe I could get a job as a lab technician or something, or just volunteer in someone's lab, while working full-time elsewhere, and hope they accept me for the following year. Hopefully it will not come to that!
On an unrelated note, I feel pretty shitty today. Just a head cold, I guess, but it's still pretty unpleasant. At least work is predictably stress-free this week. I think spending time at my parents freezing house tends to batter my immune system pretty hard. I wish they'd see the value of heating! (I mean, sure, it costs money...but being cold all the time messes with your health.)
I need to get cracking on my research project. I told Jake I'd have it done by the end of the break, and the break isn't all that long. I managed to leave my notes from our last meeting at home today, though, and I'm not really able to do much here without those, so I guess I'll really wade into it tomorrow. I'm not working tomorrow...I'm not really doing anything tomorrow, come to think of it, so I suppose it would be a good opportunity for me to settle down at Jittery Joes with my laptop and try to crank through this stuff.
Math for psychos
This is interesting:
a = 0.999...
10a = 9.999...
10a - a = 9.999... - 0.999...
9a = 9
a = 1
I can see why this works, but Greg's right that it's certainly counterintuitive...
a = 0.999...
10a = 9.999...
10a - a = 9.999... - 0.999...
9a = 9
a = 1
I can see why this works, but Greg's right that it's certainly counterintuitive...
Friday, December 15, 2006
VRAM woes
Well, I managed to get my RAM back from the people downstairs, but NWN2 still doesn't run well...apparently the game wants 128 megs of VRAM at a minimum (256 recommended...I mean, c'mon, who has 256??) and I only have 64, and since I have a laptop, I get the impression it would be exceptionally difficult (or just exceptionally costly) to upgrade it.
Thursday, December 14, 2006
Dangerous incompetence
So, apparently the idiots at UPS delivered my RAM to apartment 163 instead of apartment 263, and the people below us signed for the package and have been holding on to it for 10 days. They don't answer their door and there is no way to get their phone number, and management refuses to call them to let them know what is going on. UPS is maddeningly complacent about it, and says, We'll send a driver by the apartment sometime soon. Well, thanks.
I am going to be pissed if I can't get my RAM back. I paid over $100 for that stick.
I am going to be pissed if I can't get my RAM back. I paid over $100 for that stick.
The madness ends!
THE SEMESTER IS OVER!!!
The QM final was a really friggin hard test, but I think I managed to do ok. Whether 'ok' equals an A or a B remains to be seen, but whatever: it's over.
One thing that really sucks today is that all my friends in my physics classes are going out and gorging themselves on sushi downtown, and then getting wasted all afternoon, while I'm languishing here at work. Sigh. I thought I'd be able to get my shift off, but no luck there...
This job is pretty boring when you don't have any studying to do, I have to say. Not that I want to be studying, mind you... But I'm just sitting here, bored. Really glad that finals are over, though. I wish I had brought my laptop with me.
The QM final was a really friggin hard test, but I think I managed to do ok. Whether 'ok' equals an A or a B remains to be seen, but whatever: it's over.
One thing that really sucks today is that all my friends in my physics classes are going out and gorging themselves on sushi downtown, and then getting wasted all afternoon, while I'm languishing here at work. Sigh. I thought I'd be able to get my shift off, but no luck there...
This job is pretty boring when you don't have any studying to do, I have to say. Not that I want to be studying, mind you... But I'm just sitting here, bored. Really glad that finals are over, though. I wish I had brought my laptop with me.
Tuesday, December 12, 2006
You know...
People with Southern accents don't bother me.
People with fake Southern accents bother me.
People with fake Southern accents bother me.
Who knew?
So evidently getting 3.5 (+ a short afternoon nap) hours of sleep, then waking up at 7:30 and studying intense mathematics for thirteen and a half hours straight is, like, a really bad idea.
2.5 more hours to go. I think I've reached the point where my tiredness is making what I'm studying make progressively less sense as I go on...
Note to self: no more 16 hour shifts, please.
2.5 more hours to go. I think I've reached the point where my tiredness is making what I'm studying make progressively less sense as I go on...
Note to self: no more 16 hour shifts, please.
Rhetorical whine
Has there ever been anything so tedious and pointless as writing proofs for abstract commutation relations that have already been proven?
Monday, December 11, 2006
The daily blarg
Oddly, it seems like my biggest weakness in the QM homework has been on finite-dimensional eigenvector/eigenvalue problems. I thought I had this crap down cold! Bleh. During my incredible endless shift tomorrow one thing I'm going to have to do is bring along my old linear algebra materials and refresh my memory of this material...
Sunday, December 10, 2006
Eigenwhat?
Here's a puzzling fact mentioned in my quantum mechanics text: the eigenvectors of a hermitian transformation span the vector space. The text doesn't mention what the proof of this is, but he does say that it doesn't carry over to infinite-dimensional vector space (such as the Hilbert function space in which wave functions reside).
When I have a little free time, I'm going to look up a) what is the proof, and b) why doesn't it work for infinite-dimensional vector spaces?
When I have a little free time, I'm going to look up a) what is the proof, and b) why doesn't it work for infinite-dimensional vector spaces?
Pre-panic
I'm really worried about my quantum mechanics final. It's not until Thursday morning, so I have a few days to study for it, but still... I don't think my understanding of this material is as deep as it really should be, and I think my understanding of the material in the book is actually better than what he's taught in class, and a lot of the stuff he's gone over since the last exam was this really hard-core operator theory that is just barely even discussed at all in the textbook. I've printed out the notes, so I need to go over those, and work through the examples.
Here's my rough schedule for the next few days: tonight, finish re-reading through chapter 3 in the book, and do a quick read-through of the notes. Hopefully I will read through the stuff and mostly think to myself, aha, right, I get this stuff... So that gives me Monday to work through all of the example problems he discussed in the notes since the first exam, and on Tuesday I'm going to review the homeworks since the last test, and try to focus on anything I didn't really understand. I'm going to try to get in touch with some other people in my class for Wednesday, and hopefully a group of us can get together that day and try to tackle whatever's left.
I am really looking forward to the end of the semester. Colin and I went out to Rusan's for lunch today (yum!), and stopped by Best Buy while we were out, and I picked up a copy of Neverwinter Nights 2. I'm definitely not even installing it until finals are over, but I can't wait to try it out! I'm going to get back into my research some more after finals, but I think I'll give myself a few days to a week just to unwind, post-semester, before I get back in touch with my advisor and let him know that I'm back to the grind.
As for next semester...3 hours? Or 12? Bleh. My indecision is killing me. I think what I might end up doing is taking the two physics courses, math biology, and dropping the bioinformatics/modeling lab, which I've heard is a pretty tedious experience...this wouldn't be that surprising, since it's normally a major requirement for genetics majors (who are not involved in undergrad research), so, like most major required courses, it's likely to be pretty standardized and un-fun. I think I might be better served by taking 9 hours instead, and just spending more time doing volunteer theory work with Jake. Also, since I only need one of the physics courses (although I'd really like to take both), I can always see if Nakayama's teaching style really doesn't appeal to me, and if it doesn't, I can drop it within the first week, and get the tuition money back. I would like to take E&M to its conclusion, though, if at all possible. Someone with a degree in physics really should have studied Maxwell's equations, after all.
Here's my rough schedule for the next few days: tonight, finish re-reading through chapter 3 in the book, and do a quick read-through of the notes. Hopefully I will read through the stuff and mostly think to myself, aha, right, I get this stuff... So that gives me Monday to work through all of the example problems he discussed in the notes since the first exam, and on Tuesday I'm going to review the homeworks since the last test, and try to focus on anything I didn't really understand. I'm going to try to get in touch with some other people in my class for Wednesday, and hopefully a group of us can get together that day and try to tackle whatever's left.
I am really looking forward to the end of the semester. Colin and I went out to Rusan's for lunch today (yum!), and stopped by Best Buy while we were out, and I picked up a copy of Neverwinter Nights 2. I'm definitely not even installing it until finals are over, but I can't wait to try it out! I'm going to get back into my research some more after finals, but I think I'll give myself a few days to a week just to unwind, post-semester, before I get back in touch with my advisor and let him know that I'm back to the grind.
As for next semester...3 hours? Or 12? Bleh. My indecision is killing me. I think what I might end up doing is taking the two physics courses, math biology, and dropping the bioinformatics/modeling lab, which I've heard is a pretty tedious experience...this wouldn't be that surprising, since it's normally a major requirement for genetics majors (who are not involved in undergrad research), so, like most major required courses, it's likely to be pretty standardized and un-fun. I think I might be better served by taking 9 hours instead, and just spending more time doing volunteer theory work with Jake. Also, since I only need one of the physics courses (although I'd really like to take both), I can always see if Nakayama's teaching style really doesn't appeal to me, and if it doesn't, I can drop it within the first week, and get the tuition money back. I would like to take E&M to its conclusion, though, if at all possible. Someone with a degree in physics really should have studied Maxwell's equations, after all.
Friday, December 08, 2006
Thursday, December 07, 2006
Water on Mars?
The Global Surveyor has made an astonishing discovery: evidence of water flowing on Mars, at least twice in the past seven years.
I'm not sure why this isn't being more widely reported on...seems like a huge deal.
I'm not sure why this isn't being more widely reported on...seems like a huge deal.
Wednesday, December 06, 2006
Miniblarg
E&M is over!
Now, just need to knock out test 2 and the final (both take homes, so no biggie), and that class is done for good. Apparently we do not have any kind of final for my solid state class, so we've got today's presentations (I already gave mine...har!), then the remainder of the presentations on Monday at noon, then we're just done. Nice.
So, Isabel is actually apparently coming into town...so I guess I'm kicking the two emag tests down the road to Thursday. If I can finish both of those on the same day, I should be in good shape for an insane study marathon for my quantum final, which, of course, will be murderously hard.
On a side note, found out yesterday that one of my roommates hasn't paid his rent for the past three months. He's insisting that he's going to take care of it...still, this is a bit worrisome, because we're all on the lease together, so if he falls behind like this, we all get saddled with late fees until we're all paid up.
I think next semester I'm going to try to incorporate some light weight-lifting and ab work at Ramsey into my schedule. My current running-only workout schedule is obviously not adequate to keep the chub under control. My weight is back up to 185, which is no good. I'm 5'10", and although I apparently 'carry the weight well,' I still think anything above 180 is unhealthy.
Incidentally, I've decided to coin a new word, 'blarg': a frustrated blog post. Hence the title.
Now, just need to knock out test 2 and the final (both take homes, so no biggie), and that class is done for good. Apparently we do not have any kind of final for my solid state class, so we've got today's presentations (I already gave mine...har!), then the remainder of the presentations on Monday at noon, then we're just done. Nice.
So, Isabel is actually apparently coming into town...so I guess I'm kicking the two emag tests down the road to Thursday. If I can finish both of those on the same day, I should be in good shape for an insane study marathon for my quantum final, which, of course, will be murderously hard.
On a side note, found out yesterday that one of my roommates hasn't paid his rent for the past three months. He's insisting that he's going to take care of it...still, this is a bit worrisome, because we're all on the lease together, so if he falls behind like this, we all get saddled with late fees until we're all paid up.
I think next semester I'm going to try to incorporate some light weight-lifting and ab work at Ramsey into my schedule. My current running-only workout schedule is obviously not adequate to keep the chub under control. My weight is back up to 185, which is no good. I'm 5'10", and although I apparently 'carry the weight well,' I still think anything above 180 is unhealthy.
Incidentally, I've decided to coin a new word, 'blarg': a frustrated blog post. Hence the title.
Tuesday, December 05, 2006
Crunch time!
Got the E&M test number 2...think I'm gonna hold off starting this bad boy until Thursday or Friday. I really want to take a day off tomorrow, and Isabel might be coming into town, so that would be fun, to hang out with her one last time before she takes off for DC for good... I guess I'll take the day off if Isabel comes, and I won't if she doesn't.
Last classes tomorrow. Woo! One semester down, one to go... And since I did so frickin good on the 4th Stat test, I don't have to take the final at all. Snap indeed.
So let's see...I need to knock out this E&M test on say Thursday, which will be good, I can spend my 6 hour shift on Thursday doing that. I also need to do the take-home final for E&M at some point...I'm not sure when we're getting that. Need to ask him about that tomorrow in class. I can probably knock that and the test 2 out in an all-day E&M-fest on Thursday. I'm not sure if we're having a take-home final for solid state...it sounds like we might not, so I guess the final project might've been it. A little worried about that class...what's he going to base our grades on??
So starting on Friday, I'm doing ALL QUANTUM MECHANICS, ALL THE TIME! I'm actually looking forward to that, believe it or not. I'm going to re-read what we've done in the book (which is only 3 chapters, really) - I can spend Friday and Saturday knocking that out, then on Sunday I'll work my way through his in-class examples. That leaves me Monday through Wednesday to review homework and the old tests.
Last classes tomorrow. Woo! One semester down, one to go... And since I did so frickin good on the 4th Stat test, I don't have to take the final at all. Snap indeed.
So let's see...I need to knock out this E&M test on say Thursday, which will be good, I can spend my 6 hour shift on Thursday doing that. I also need to do the take-home final for E&M at some point...I'm not sure when we're getting that. Need to ask him about that tomorrow in class. I can probably knock that and the test 2 out in an all-day E&M-fest on Thursday. I'm not sure if we're having a take-home final for solid state...it sounds like we might not, so I guess the final project might've been it. A little worried about that class...what's he going to base our grades on??
So starting on Friday, I'm doing ALL QUANTUM MECHANICS, ALL THE TIME! I'm actually looking forward to that, believe it or not. I'm going to re-read what we've done in the book (which is only 3 chapters, really) - I can spend Friday and Saturday knocking that out, then on Sunday I'll work my way through his in-class examples. That leaves me Monday through Wednesday to review homework and the old tests.
The morning booyah
Quantum mechanics is OVER! Booyah. Well, except for the final, natch.
Let's see...gotta run down and deposit my paycheck this morning, then go to the Fred building to ask about direct deposit, then grab a quick lunch, then go to business services and pay for my spring tuition, then work till 4, then gotta pay my rent before 5.
Busy busy busy...I really need to review for E&M and Quantum, I feel so, so, so behind...
Let's see...gotta run down and deposit my paycheck this morning, then go to the Fred building to ask about direct deposit, then grab a quick lunch, then go to business services and pay for my spring tuition, then work till 4, then gotta pay my rent before 5.
Busy busy busy...I really need to review for E&M and Quantum, I feel so, so, so behind...
Monday, December 04, 2006
End-of-semester rant
My solid state presentation went well. I felt like I had a smooth delivery, I sounded like I knew what I was talking about (heh heh), and my slides looked good. One thing was that the audience looked terribly, terribly bored. Ah well. I'm pretty sure I didn't exceed my 15 minute alloted time, so I'm not to blame! I did my best to make the material interesting...even though, let's face it, it was some incredibly dry stuff.
I've got my final (I think it's my final...) Electricity and Magnetism homework assignment due at midnight (!) tonight, and some of these problems are a little confusing. Going to have to stop writing on here and get cracking if I'm gonna get that in under the wire... Also my Quantum homework is due tomorrow morning. Blargh!
I've only got 1 real final this semester (Quantum Mechanics), so I'm pretty relieved about that, and it's on the very last day of finals, so I'm going to be the most prepared student in that frickin class. I'm worried about the final anyway, though, because the only other real grade we've had in there (aside from our piddly 10% homework grade) is the midterm...I did well on the midterm, but if I screw up the final, everything goes down the tubes anyway. So there's some pressure there.
I think we have finals in my Electricity and Magnetism and Condensed Matter classes (actually, I really have no idea whatsoever about my CM class), but he's said it'll be a take-home final, so I'm not too worried about that. It'll probably be a fair amount of work, but there's no sense stressing out about a take-home, right?
So, I've got my spring semester schedule all figured out. Yes, I'm taking a 12-hour load of classes again, even though I only need 3 hours to graduate! (WTF is wrong with me? I'm not sure.) I'm taking Electricity and Magnetism II, Quantum Mechanics II, Mathematical Biology, and Bioinformatics and Modeling Lab. Believe it or not, I'm really looking forward to next semester's courses.
This winter break, I'm gonna try to finish up that Waddington MET model I was working on before finals-season set in. Maybe I can get a second publication out of it! It's too late for it to matter for grad school applications, but, as they say, 'publish or perish.'
I've got my final (I think it's my final...) Electricity and Magnetism homework assignment due at midnight (!) tonight, and some of these problems are a little confusing. Going to have to stop writing on here and get cracking if I'm gonna get that in under the wire... Also my Quantum homework is due tomorrow morning. Blargh!
I've only got 1 real final this semester (Quantum Mechanics), so I'm pretty relieved about that, and it's on the very last day of finals, so I'm going to be the most prepared student in that frickin class. I'm worried about the final anyway, though, because the only other real grade we've had in there (aside from our piddly 10% homework grade) is the midterm...I did well on the midterm, but if I screw up the final, everything goes down the tubes anyway. So there's some pressure there.
I think we have finals in my Electricity and Magnetism and Condensed Matter classes (actually, I really have no idea whatsoever about my CM class), but he's said it'll be a take-home final, so I'm not too worried about that. It'll probably be a fair amount of work, but there's no sense stressing out about a take-home, right?
So, I've got my spring semester schedule all figured out. Yes, I'm taking a 12-hour load of classes again, even though I only need 3 hours to graduate! (WTF is wrong with me? I'm not sure.) I'm taking Electricity and Magnetism II, Quantum Mechanics II, Mathematical Biology, and Bioinformatics and Modeling Lab. Believe it or not, I'm really looking forward to next semester's courses.
This winter break, I'm gonna try to finish up that Waddington MET model I was working on before finals-season set in. Maybe I can get a second publication out of it! It's too late for it to matter for grad school applications, but, as they say, 'publish or perish.'
Saturday, December 02, 2006
Bandgapalicious
So, one thing I realized about my solid state physics class is that I really have managed to avoid learning the essential material for most of the semester. I've been reading ahead in my quantum book, and finally got to the stuff that makes the really really basic solid state stuff (that we did back in friggin' August) make some sense: for example, where do bandstructures come from? Turns out they arise (at least, in the theory) from a very technical point in Bloch's theorem (which was not at all well explained by our textbook). But at least it makes sense now. To wit:
If V(x+a)=V(x) (periodicity), then the V(x) that satisfy the TISE H*psi(x)=E_n*psi(x) follow the eigenfunction condition psi(x+a)=exp(i*K*a)*psi(x). If you use V(x) as a series of evenly spaced delta functions and use this to find the eigenfunctions, you end up with an expression for k (and therefore E), where your result is:
cos(K*a)=cos(k*a)+(m*alpha)/[(hbar^2*k)*sin(k*a)]
Since |cos(K*a)|<=1, you get a set of allowed k values: whenever the RHS of the above equation > 1, you get a 'forbidden zone' for k, which tells you what energies aren't allowed. This is where bandgaps come from.
Finishing up my solid state project this weekend. I think I mostly get what's going on...hope so, anyway. I wonder if we're going to even have a final in this class.
If V(x+a)=V(x) (periodicity), then the V(x) that satisfy the TISE H*psi(x)=E_n*psi(x) follow the eigenfunction condition psi(x+a)=exp(i*K*a)*psi(x). If you use V(x) as a series of evenly spaced delta functions and use this to find the eigenfunctions, you end up with an expression for k (and therefore E), where your result is:
cos(K*a)=cos(k*a)+(m*alpha)/[(hbar^2*k)*sin(k*a)]
Since |cos(K*a)|<=1, you get a set of allowed k values: whenever the RHS of the above equation > 1, you get a 'forbidden zone' for k, which tells you what energies aren't allowed. This is where bandgaps come from.
Finishing up my solid state project this weekend. I think I mostly get what's going on...hope so, anyway. I wonder if we're going to even have a final in this class.
Let the yammering begin
I thought I'd start a blog where I could yammer about the stuff I'm learning in my classes. Seems random, but I think reprocessing the information by typing it down helps me learn the stuff better...and doing it semi-publically makes me feel a semi-obligation to do so.
This probably won't begin in earnest until next semester. Just getting a jump on things.
This probably won't begin in earnest until next semester. Just getting a jump on things.
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