Register to reply 
Physical Chemistry/Quantum Mechanics Eigenvalues 
Share this thread: 
#1
Jan2413, 05:01 PM

P: 2

1. The problem statement, all variables and given/known data
Indicate which of the following expressions yield eigenvalue equations and identify the eigenvalue. a) d/dx (sin(∏x/2)) b) i*hbar * ∂/∂x (sin(∏x/2)) c) ∂/∂x (ex^2) 3. The attempt at a solution I know that if the wave equation yields an eigenvalue equation, it will give me the wave equation multiplied by the eigenvalue back. I calculated the derivatives: a) 1/2∏cos(∏x/2) b)(i*hbar∏/2)(cos(∏x/2)) c) 2x Because none of these give me back the original wave function, does that mean none of these are eigenvalue equations? I don't think my professor would give us a problem that asks to calculate the eigenvalues, where there are no eigenvalues. In parts A and B, the ∏x/2 is in both the question and the answer, but the sin changes to cosine when you take the derivative, so does that mean it is not an eigenfunction? Any help would be appreciated. 


#2
Jan2413, 06:17 PM

HW Helper
Thanks
PF Gold
P: 7,632

That seems like an unusual way to phrase the question. Are you really asking whether any of those functions satisfy ##y''+\lambda y = 0##? Note the second derivative, not just the first.



#3
Jan2413, 06:22 PM

P: 2

I dont think so. I have taken a differential equations course and I have not seen eigenvalues in the context he is asking for before. From my notes, using the schroedinger wave equation (time independent), you can use the Hamiltonian operator on a wave function, and if the wave exists, after using the Hamiltonian, you get the energy of the wave multiplied by the wave function. Therefore, I should get the wave function back in my answers and what he is calling the "eigenvalue" is the energy of the system. Is that any clearer?
Edit: Oops, I just realized I posted in the math section. 


#4
Jan2413, 09:00 PM

HW Helper
Thanks
PF Gold
P: 7,632

Physical Chemistry/Quantum Mechanics Eigenvalues
Well, I don't know about that physics stuff, so it may in fact be clearer, but not to me. But sines and cosines do give multiples of themselves back on differentiating twice. For example, this shows up solving the one dimensional wave equation for a vibrating string with fixed ends, where they are the eigenfunctions. That's why I speculated as I did in post #2. But I will leave it to one of the resident physicists to actually answer your question.



#5
Jan2413, 10:14 PM

Sci Advisor
HW Helper
Thanks
P: 25,228

There's no way to say whether a function is an eigenfunction until you say what operator they are supposed to be an eigenfunction of. Every function is eigenfunction of the identity operator. What hamiltonian are you talking about? If the operator part is supposed to be the d/dx and the rest of the expression the eigenvector then I'd agree none of them are eigenvectors. Pretty badly phrased question.



Register to reply 
Related Discussions  
Quantum Mechanics, Schrodinger equations and energy eigenvalues  Introductory Physics Homework  1  
Physical Chemistry vs Statistical Mechanics notation  Chemistry  8  
Quantum Mechanics.. Operators, Hermitian and Eigenvalues  Advanced Physics Homework  1  
Quantum Theory (physical chemistry)  Biology, Chemistry & Other Homework  1  
Taking Physical Chemistry before formally taking Quantum Mechanics  Academic Guidance  17 