Recent content by jmm5872

A hydrogen atom is in its ground state and is subject to an external electric field of E = ε(\hat{x}+\hat{y}+2\hat{z})e-t/\tau I'm confused as to how to compute the matrix elements of the perturbed hamiltonian since this is not in the z direction. Would I have to do something like this...

I have calculated a k-space function to be f(k) = \frac{1}{2k} I want to Fourier transform this to find f(x), I have found many different Fourier transform equations...can I use this one? f(x) = \frac{1}{\sqrt{2π}}\int\frac{1}{2k}e-ikxdk Limits fo integration -Infinity to Infinity...

Sorry, I just realized I need to take the Latent heat of melting and make it negative for freezing...this solves my first problem.

Entropy of molten lead "freezing" Lead melts at 327.5 C.° The latent heat of melting of lead is 24.1 J/g, and the heat capacity of solid lead is 0.14 J/g °C. You take 100 grams of molten lead at a temperature of 327.5 C° and pour it on the sidewalk. The lead freezes and then comes into thermal...

Two particles with equal mass m are confined by a harmonic oscillator potential of frequency ω. Assume that we somehow know that there is one particle in the first excited state and one in the second excited state. What is the probability of finding both particles within a certain distance if...

I figured out the problem, and it was a little bitter-sweet. The above integral was to get a c3(t) coefficient. I already solved for the c1(t) and c2(t) previously, and they all contained the same A and B unknowns. I also had the initial condition of c1(0)=0, so I was able to solve for A in...

Thank you for rewriting my integral Simon! What you have written is correct, except for the upper limit of the integrand is actually e^-Ht. As for a closed form solution, I am not quite sure. The original paper I am trying to work off does a more complicated problem in which H and k are not...

I have been working through a method of solving the Time-Dependent Schrödinger Equation. I'm trying to learn this techniques before I actually jump into my project, however, I have come to an integral that I have been trying to do but can't think of a way to approach it. Mathematica could not...

A wave packet of mean energy E0 is incident on a potential square barrier. The figure below shows stills from a film showing 9 successive stages in interaction. a) True or false? The incident packet at time t = 0 describes many particles, each in a different momentum state. If false, tell...

I just have a simple question to get me started. If I am given an initial value wavefunction ψ(x,0) and I am asked to find <P> at t = 0 can I use this: <P> = -ih∫ψ*(x,0)\frac{∂}{∂x}ψ(x,0)dx or do I need to find ψ(x,t) before I find <P>?

V(x) = |g| (δ(x+L)+δ(x-L) Consider scattering from a repulsive twin-delta function potential. Calculate R and T. I'm mostly confused about computing the T coefficients for multiple barriers. Would I compute the T coefficient for the barrier at x = -L and at x = L separately? Then...

Ah, okay, I understand now. I forgot that the potential is opposite the sign of force! Thank you! F = -dU/dx

The problem specifically states that k > 0, and F = kx, which gives U = 1/2 kx^2. I don't really understand what you are trying to say, or where the F = -kx that you wrote comes from.

Consider a mass m confined to the x-axis and subject to a force Fx=kx where k>0. Write down and sketch the potential energy U(x) and describe the possible motions of the mass. (Distinguish between the cases that E>0 and E<0. It is the part in parenthesis that confuses me. I can't...

I am just trying to get the conceptual basics in my head. Can I think of things this way... If you are taking the integral of a function f(z) along a curve γ in a region A. If the curve is closed and f(z) is analytic on the entire curve as well as everywhere inside the curve, then the...