Recent content by arenaninja

Thanks a lot mathfeel. It took me a while when you mentioned the hermicity of the Hamiltonian, but after staring it down for a straight 5 minutes I felt dumb since it's so obvious, hahaha.

Homework Statement Use [H_{0},r_{j}]=\frac{i\hbar}{\mu}p_{j} for the Hydrogen atom (where the j's denote the jth components in Cartesian coordinates) to prove that <n_{f},l_{f},m_{l,f}|p_{j}|n_{i},l_{i},m_{l,i}>=-i\mu\omega<n_{f},l_{f},m_{l,f}|r_{j}|n_{i},l_{i},m_{l,i}> Homework...

Homework Statement An ideal particle of energy E is incident upon a rectangular barrier of width 2a and height V_{0}. Imagine adjusting the barrier width and height so that it approaches V(x)=\alpha \delta(x). What is the relationship between V0, alpha and a? Homework Equations The...

Homework Statement Derive the hypsometric equation, assuming a sea level temperature of 15 C, and that the temperature decreases with heigh at a rate of 6.5 C per km. Homework Equations Ideal gas law: P=\rho RT Hydrostatic equilibrium: dP = -\rho gdz Temperature varies with height: T...

ahhh, that's right. Thanks a lot, it makes a lot more sense from your first sentence and I can make some more progress on this one now.

Homework Statement Find the transmission coefficient for the potential V(x)=-\alpha\left[\delta\left(x+a\right)+\delta\left(x-a\right)\right], where alpha and a are positive constants. Homework Equations T \equiv \frac{\left|F\right|^{2}}{\left|A\right|^{2}} The Attempt at a Solution...

I searched some Fourier transform tables on the web (even saw the one in wkipedia) but frankly I couldn't discern the one that applied to this case (in fact I thought most of them do not look very similar). fzero, thanks for the suggestion. I think I see where I could go with this. So the...

Homework Statement Given \Psi(x,0)=\frac{A}{x^{2}+a^{2}}, (-\inf<x<\inf) a) determine A c) find the momentum space wave function \Phi(p,0), and check that it is normalized Homework Equations At t=0, we can find the momentum space wave function by the formula...

Well since I was using ladder operators I was eventually left with <\Psi_{n}|H\Psi_{n}>=const*<\Psi_{n}|(2n+1)\Psi_{n}>, and here I used the fact that the time dependence wouldn't matter in the inner product (since, once I take out 2n+1, it must be 1) Part b) is actually "b) At some time...

Homework Statement A particle mass m in the harmonic oscillator potential starts out in the state \psi(x,0)=A\left(1-2\sqrt(\frac{m\omega}{\hbar})x\right)^{2}e^{\frac{-m\omega}{2\hbar}x^{2}} for some constant A. a) What is the expectation value of the energy? b) At some time later T the wave...

ahh you're right. So if I'm interpreting this correctly according to E_{n}^{\omega}= \left(n+\frac{1}{2}\right)\hbar\omega, \hbar\omega/2 will not be found. thanks!

Homework Statement A particle in the ground state of the harmonic oscillator with classical frequency \omega, when the spring const quadruples (so \omega^{'}=2\omega) without initially changing the wave function. What is the probability that a measurement of the energy would still return the...

Ahh ok. Your first sentence explains it. Many thanks!

Hey everyone. I'm trying to refresh myself of solving linear ODEs. For simplicity's sake, I began by trying to solve xy'=xy+y This is actually a separable ODE, and the solution is y = c_{1}xe^{x}. I am attempting to derive the same result from a series solution. First, rewrite this as a...

PV = nRT Also, for ideal gases: c_{P} = c_{V} + nR Ohhh I see (I think). So the last term: nk_{B}T = c_{P}T - c_{V}T I'm guessing c_{V}T = s_{0}T. Great! Thank you very much!