quatum physics help

[theChris]

ok, i'm in a modern physics class and have homework due monday. we are doing quantum physics ect... the questions are over the hydrogen atom. most of the questions involve finding an expectation value for a wave function in spherical coordinates. I am not completly sure how to do this. it asks for the expected value of V(r), (Voltage? Volume?). i tried with just the R(r) function, but i get a negative value with a HUGE magnitude. so i tried the tripleintegeral and got a smaller positive value. i assume this is correct.

next, what is a "pattern of splitting". its on a question but not defined in the notes.

what is the eigenfunction (or vlaue?) for r and r^2? is it just r and r^2?

i have a question about the eigenvalue of Lz = ih d/dphi, and i get the awnser given multplied by e^(i ml phi), do you assume ml to be 0, or is there a reason i ml phi = 0?

also, the eigenfunction for V(r) is listed with a term e^2. is this euler's numebr, or the charge of an electron?

I really hate how vauge the notes are. every question is over applying all of the concepts to something and never as hard as what is taught in the class or given in the notes...

in any case, help would be appreciated.

[Sch3mat1c]

Sounds like you should've been awake during class..

But anyway, that's over even my head...and probably 99.9% of everyone else here... I'm suprised any one here is into quantum physics, heh

Tim

[DIY_Peter]

I would suggest getting a book about quantum physics.

A very good one is "quantum Physics" by Stephen Gasiorowicz.
It minimises the amount of math needed, but don't think you will be able to understand quantum mechanics without a good knowlidge of math.

V(r) is the potential energy in function of the distance from the atom's centre.

V(r)=-(Ze^2)/r

The rest of your questions are not very clear. You really should do some reading about it. the complete description of the hydrogen atom problem can be found in the book I mentioned.
There is no real easy way of explaining these things. you have to understand all of it, not just parts.

Have fun!

[Circlotron]

Quantum physicists probably hate analogue cct theory and love D/A converters.

[phonon]

it asks for the expected value of V(r), (Voltage? Volume?). i tried with just the R(r) function, but i get a negative value with a HUGE magnitude. so i tried the tripleintegeral and got a smaller positive value. i assume this is correct.

The "expectation value" of "X" is the value of "X" that a particle with wavefunction phi will have on average. The expectation value of "X" is

integral(phi* X phi, over all space)

where phi* is the complex conjugate of phi. This works for any "X," whether it be the position, velociy, angular momentum, or the potential as in your problem, etc.
(phi* phi) is the probability that a particle is at a certain position, so what you are doing in the preceding integral is adding up the (probability of the particle being at a certain point)*(value of X at that point), a "weighted average," which is the expectation value.

also, the eigenfunction for V(r) is listed with a term e^2. is this euler's numebr, or the charge of an electron

here, e is the electron charge. As a general hint for guessing which "e" is meant, if it appears with a constant exponent, such as "e" or "e^2" or "e^(1/2)," etc. it is the electron charge; if it appears with a variable exponent, such as "e^(i pi x^2)" or "e^(-x/kT), etc. it is e~2.7182818284590452.

If you have calculus and aren't confused by the concept of differential equations, the book "Quantum Physics" by Eisberg and Resnick is the classic introductory text. It is probably a bit much for helping you with an overview of modern physics course, but if you really want to understand the subject, it is a good text.

[Ryder]

I do not have the expertise to answer such Q though I usually enjoy trying to follow. I am glad to see someone here does.

Below is another couple Google forums that are actually quite good if you do not already know of them. Both the electronics and physics sections.

Hope they are helpful.

http://groups.google.com/groups?hl=e...TF-8&group=sci


Craig Ryder

[grataku]

Originally posted by theChris
ok, i'm in a modern physics class and have homework due monday. we are doing quantum physics ect... the questions are over the hydrogen atom. most of the questions involve finding an expectation value for a wave function in spherical coordinates. I am not completly sure how to do this. it asks for the expected value of V(r), (Voltage? Volume?). i tried with just the R(r) function, but i get a negative value with a HUGE magnitude. so i tried the tripleintegeral and got a smaller positive value. i assume this is correct.

next, what is a "pattern of splitting". its on a question but not defined in the notes.

what is the eigenfunction (or vlaue?) for r and r^2? is it just r and r^2?

i have a question about the eigenvalue of Lz = ih d/dphi, and i get the awnser given multplied by e^(i ml phi), do you assume ml to be 0, or is there a reason i ml phi = 0?

also, the eigenfunction for V(r) is listed with a term e^2. is this euler's numebr, or the charge of an electron?

I really hate how vauge the notes are. every question is over applying all of the concepts to something and never as hard as what is taught in the class or given in the notes...

in any case, help would be appreciated.

At this point in the semester you should be familiar with the Schroedinger equation and what its elements are: eigenvalues, eigenstates and Hamiltonian operator, the expectation value <psi|H|psi> which is the avg result of many experimental observation. Basically, how populated is each eigenstate.
Anyway, forget the notes, get yourself a few quantum books and see how it's done.
I just have a hard time believing they would start you off with the hydrogen atom instead of things like the particle in the box, harmonic oscillator and stuff like that, at least they should have defined potential and kinetic term properly. I suspect the problem maybe student related rather than course related. Am I right or am I right?

[phonon]

this might or might not be helpful:

if you have an operator, Z, then if for some function f,
Z(f) = k*f, where k is some constant,
then f is an eigenfunction of Z, and k is the eigenvalue of Z corresponding to f.

For example, let the operator Z=x*d[]/dx, so Z(f)=x*d[f]/dx. For f=x^2, Z(f)=x*d[x^2]/dx=x*2x=2*x^2=2f, so x^2 is an eigenfunction of Z and its eigenvalue is 2. Similarly, x^n is also an eigenfunction of Z, with n as its eigenvalue.

In your case, you are just working with the z-component of angular momentum operator, Lz=i*hbar*d[]/d[phi]; the idea is basically the same.

[SY]

"Pattern of splitting" must have been asked in the context of the presence of an electric or a magnetic field. Which was it? Once you know that. you're home free.

The angular momentum question is also pretty easy once you realize that the wavefunction is expressable as a product of a radial function (a constant times a Laguerre polynomial) and a spherical harmonic. That's because, when you put the Hamiltonian in spherical coordinates, it's separable into a radial and an angular part. The solution to the angular part is the series of spherical harmonics.

The hydrogen atom is worked out in exquisite detail in nearly any QM text. If you don't already have the Feynman Lectures, you should run, not walk, and buy them. H-atom is worked out in volume III. The splittings are also dealt with in a neat (i.e., not using perturbation theory) way.

[theChris]

hmm, well i'm not big into quantum by any means, but i gotta pass the class, well actually maby not, bizzarly they're thinking of offering the option of replacing the requirement with a class that i'm taking anyways!

Ok, so the wave function is always integrated over space. that helps, but not entirely. i got (r^2) to be 0, and delta r to be 0. that seems a little odd IMO.

and yes the pattern was in a magnetic feild, but i don't know what pattern he's talking about, like a pattern of photon-lines, or a pattern of energy levels, or such.

this class moves too fast to get into detail on any subject for long. we have to do relativiety, particle motion of waves, wave motion of particles, uncertinty, schrodinger equation, quantum physics and if time permits solid state physics. the teacher says that is the one part of the class the EEs use most. ironically the entire class is made up of over 80% EE majors... you are a little correct though, i pretty much don't study the notes and book 24/7, but i'm not a physics major. i just need a C and i'm fine. since i wasn't good with mechanical physics, i'm not too good at relating all the kinetic energy to momentum ect... and the notes bring up new terms without defining them. like frequency being v, and h-bar being differnt then h.

and i have to study for history cause the teacher for that class teaches it like the 50 people in it are history majors...