0
votes
0answers
22 views

WKB transmission probability in momentum space

What is the expression for the WKB transmission probability in momentum space?
6
votes
3answers
168 views

Finding the energy eigenvalues of Hydrogen using WKB approach

I need help to find the energy eigen values of Hydrogen atom using WKB approach. So far I know, the radial equation is given by $$\frac{1}{r^2} \frac{\partial }{\partial r} \left( r^2 \frac{\partial ...
1
vote
1answer
164 views

How to use the WKB approximation to find wave functions?

I'm trying to learn how to apply WKB. I asked a similar question already, but that question was related to finding the energies. Here, I would like to understand how to find the wave functions using ...
1
vote
1answer
339 views

How to apply the WKB approximation in this case?

I'm trying to learn how to apply the WKB approximation. Given the following problem: An electron, say, in the nuclear potential $$U(r)=\begin{cases} & -U_{0} \;\;\;\;\;\;\text{ if } r < ...
1
vote
2answers
132 views

Complex Versus Real Wave Velocities in Quantum Mechanics

There's a fantastic quote in Schrodinger's second 1926 paper1 that apparently provides some motivation for the discrete energy levels (I think) that I'm having trouble interpreting: I would not ...
4
votes
1answer
376 views

Bohr-Sommerfeld quantization from the WKB approximation

How can one prove the Bohr-Sommerfeld quantization formula $$ \oint p~dq ~=~2\pi n \hbar $$ from the WKB ansatz solution $$\Psi(x)~=~e^{iS(x)/ \hbar}$$ for the Schroedinger equation? With $S$ the ...
5
votes
0answers
131 views

Looking for modern results in semiclassical physics and relevant references

What are some important approximations, especially those that are state-of-the-art, used to approximate the many-body dynamics of atoms and molecules in the semiclassical regime? To be clear, I'm not ...
3
votes
1answer
470 views

Bohr-van Leeuwen theorem and quantum mechanics

Preamble: If one considers an ideal gas of non interacting charged particles of charge $q$ in a uniform magnetic field $\mathbf{B} = \mathbf{\nabla} \wedge \mathbf{A}$, then the classical partition ...
3
votes
1answer
440 views

Alkali atom in oscilating electromagnetic field

I am trying to calculate atom - light (EM field) interaction Hamiltonian, and the results I get seem to me rather unphysical - I get some nonzero matrix elements which should not be there. Please, can ...
1
vote
0answers
55 views

Length of the orbit (semiclassical orbits)

The Gutzwiller trace is about $$ d(E)=d_{0} (E)+ \sum_{p.o}A_{p}Cos(S(E)\ell_{p}) $$ and $ \ell_{p} $ are the length of the orbit. However my question is, how can one derive the length of the orbit ...
7
votes
1answer
232 views

Simulating the evolution of a wavepacket through a crystal lattice

I am interested simulating the evolution of an electronic wave packet through a crystal lattice which does not exhibit perfect translational symmetry. Specifically, in the Hamiltonian below, the ...
3
votes
1answer
241 views

Classical (or semi-classical) interpretation of photoelectric effect?

This site says that "it has recently been proven that the photoelectric effect can be interpreted classically (or at least semi-classically) in non-particle, wavelike terms". Is anyone familiar with ...
5
votes
1answer
183 views

Hawking Radiation from the WKB Approximation

Reading this paper which is itself an exposition of Parikh and Wilczek's paper, I get to a point where I fail to be able to follow the calculation. Now this is undoubtably because my calculational ...
6
votes
3answers
753 views

How does one quantize the phase-space semiclassically?

Often, when people give talks about semiclassical theories they are very shady about how quantization actually works. Usually they start with talking about a partition of $\hbar$-cells then end up ...
1
vote
0answers
62 views

spectral eigenvalue staircase and quantum system

in a d-dimensional system of Quantum physics , does the Eigenvalue staircase $ N(E)= \sum_{E_{n}\le E} 1 $ determine ALL the properties of Quantum System ?? for example, let us assume that the ...