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[marglinw]

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if function f and g are two orthonormal wavefunctions and we form a linear combination function psi = af + bg (a and b are constants not found), how do you express the normalization constant for psi as a function of a and b? This is supposed to be an easy question, but I am not good at this stuff. Thanks for any help

 

[leverp2000]

For psi to be normalized, the integral of |psi|^2 over all space should be 1. So to normalize in this case, you solve that integral and find for which values of a and b, it'll be 1.

if function f and g are two orthonormal wavefunctions and we form a linear combination function psi = af + bg (a and b are constants not found), how do you express the normalization constant for psi as a function of a and b? This is supposed to be an easy question, but I am not good at this stuff. Thanks for any help

 

[mercaptovizadeh]

I haven't seen quantum mechanics in a while, but I would say you should do the following:

1.) Multiply the linear combination by it's complex conjugate.

2.) Integrate over the space.

3.) Cross terms drop out due to orthonormality and square terms are 1 (am I right here), so you get some expression of a and b = 1.

4.) That gives you the normalization constant.

Please correct me guys if I botched this up. Also, maybe you should post this on a more frequented forum like Pre-Allopathic?

 

[leverp2000]

Yeah, so integral of f*(f) or < f | f > and < g | g > will be 1, while < f | g > and < g | f > will be 0, because its an orthonormal basis.

I haven't seen quantum mechanics in a while, but I would say you should do the following:

1.) Multiply the linear combination by it's complex conjugate.

2.) Integrate over the space.

3.) Cross terms drop out due to orthonormality and square terms are 1 (am I right here), so you get some expression of a and b = 1.

4.) That gives you the normalization constant.

Please correct me guys if I botched this up. Also, maybe you should post this on a more frequented forum like Pre-Allopathic?

 

[marglinw]

Thanks. It is just strange that the normalization constant will be a + b = 1. This is compared to a function that has two of the same constants so your normalization constant would be a = 1/sqrt(2). I guess that's it. I can always count on sdn.

 

[mercaptovizadeh]

Thanks. It is just strange that the normalization constant will be a + b = 1. This is compared to a function that has two of the same constants so your normalization constant would be a = 1/sqrt(2). I guess that's it. I can always count on sdn.

Actually, shouldn't it be a^2 + b^2 = 1?

 

[Doctor&Geek]

This whole thread just goes to show I learned nothing in quantum chemistry class, and moreover, I suck at math. 😀

 

[SaltySqueegee]

Blah blah blah... 😉

 

[JETER]

1.) Multiply the linear combination by it's complex conjugate.

2.) Integrate over the space.

3.) Cross terms drop out due to orthonormality and square terms are 1

Ah, so you were/am a physics major! BTW, your advice sounds right. BUT, we are in a med/premed forum. No one talks like that. "Complex conjugate . . . " The OP doesn't know how to normalize a function, and you throw that out there. Ha

 

[mercaptovizadeh]

Yes, I was. I went to a prestigious school, and the physics department is pretty decent, but my quantum sucks.

This is primarily because we only had one quarter of it! Most schools give you two or three or even four semesters!

So, while my statistical, E&M, and mechanics are decent, my quantum and optics suck.

Did I forget to mention that I had the same prof for quantum and optics and he was the worst? Will not forgive him.

 

[JETER]

Yeah, I guess that after one quarter, you would not be too familiar with it later. My school was just the opposite. Excellent quantum and optics, but our EM sucked. Depending on the prof, we either got a 'history of electric fields' or hell. One one semester of that for me. But, I've got 3 semesters of quantum under my belt, and one of quantum chemistry (DIFFERENT from PChem). I love how those who took first semester P-Chem in the pre-allo forum talk about all the 'quantum mechanics' they had to endure.

Were there many physics students going pre-med at your school? I was the only one in mine, so I was under the impression that it was rare. Cold determination in the lab, or on Mathematica, is a bit different from the compassion expected from MDs.

 

[mercaptovizadeh]

Yeah, I guess that after one quarter, you would not be too familiar with it later. My school was just the opposite. Excellent quantum and optics, but our EM sucked. Depending on the prof, we either got a 'history of electric fields' or hell. One one semester of that for me. But, I've got 3 semesters of quantum under my belt, and one of quantum chemistry (DIFFERENT from PChem). I love how those who took first semester P-Chem in the pre-allo forum talk about all the 'quantum mechanics' they had to endure.

Were there many physics students going pre-med at your school? I was the only one in mine, so I was under the impression that it was rare. Cold determination in the lab, or on Mathematica, is a bit different from the compassion expected from MDs.

I was the only one. I think that when I was a senior, there may have been one sophomore who also plans to be pre-med, but otherwise, we are a rare species. In contrast, I don't think physicists are at all cold: either they are arrogant b*stards or they are pretty likeable and quirky people - of course there are those who fit in neither category.

Yeah, I think our quarter system sucks: we basically had to go through Reif in 9 weeks and Griffiths (that's E&M) in the same amount of time. It was miserable. And the prof had that annoying habit of putting a trick question on every exam (there was three per exam), so that when you integrated over the charge density, or tried to find the magnetic field, it came to 0 (!). Man did that destroy people's confidence on the test.

The quantum guy is an annoying senior lecturer, who in my humble opinion, should be booted. Fortunately, they took him off quantum the year after I took it and threw him into optics (his "specialty"), which was even worse hell for me two years later.

If you don't mind my asking, are you in an MD/PhD program already, or just interested in one? I am the latter, and am having a tough time deciding between physics PhD and immunology PhD. Unfortunately, a lot of people have the impression that if you wanna do physics, you should do something relevant, like imaging or biophysics. In contrast, my interests lie in theoretical/philosophical questions of physics, but I guess it would not be great to say that I want to pursue that at an interview.

 

[mercaptovizadeh]

Also, I'm doing some self-study in my free time - have any suggestions as to good physics books to use? I've made up a list of my own:

1.) Quantum - Shankar, then Merzbacher
2.) E&M - Griffiths, then Jackson
3.) Mechanics - Marion, then Goldstein
4.) Statistical - Reif, then Landau
5.) Optics - Hecht, then Born

 

[the_one_smiley]

It's great to see other physics majors interested in MDPhD programs! Will any of you be at Stanford this Monday?

You may have read these already, but the obvious omissions from your list are the Feynman Lectures on Physics. Volume III is sort of dated, and the Shankar or Cohen-Tannoudiji/Diu/Laloe (old classic) books are much better for quantum mechanics. However, for classical mechanics and E&M, Volumes I and II are enjoyable and brilliant.

For general relativity, Dirac wrote an excellent booklet that is only about 100 pages long. For a more rigorous approach that does all the math (there are about five appendices, each with an entire graduate-level math course crammed into it), check out Wald.

 

[mercaptovizadeh]

It's great to see other physics majors interested in MDPhD programs! Will any of you be at Stanford this Monday?

You may have read these already, but the obvious omissions from your list are the Feynman Lectures on Physics. Volume III is sort of dated, and the Shankar or Cohen-Tannoudiji/Diu/Laloe (old classic) books are much better for quantum mechanics. However, for classical mechanics and E&M, Volumes I and II are enjoyable and brilliant.

For general relativity, Dirac wrote an excellent booklet that is only about 100 pages long. For a more rigorous approach that does all the math (there are about five appendices, each with an entire graduate-level math course crammed into it), check out Wald.

Gen Rel: Or Misner's Gravitation!

Btw, I am not applying this time around, will apply this coming summer.

 

[JETER]

I guess the only things that I can add to the subject are:

Statistical:
Modern Course in Statistical Physics, Reichl
Stat. Mech, McQuarrie (old, but good).

In terms of general research and reference books, you can't beat the the Dover series. If you don't already own them (only like 10 bucks a pop), check them out.

No dice on Stanford, though.