# Tagged Questions

The tag has no usage guidance.

68 views

### is there an error in this paper ¿¿

http://vixra.org/pdf/0908.0079v1.pdf see equation (2.21) the reasoning to get this (2.21) goes from page 9 to page 14 should be the inverse of the potential denoted by $x(V)$ proportional to the ...
19 views

### could we obtain the potential (in one dimension) from the Gutzwiller trace?

to solve and obtain the potential of a 1-D Hamiltonian we must solve an integral equation $$N(E)= A \int_{0}^{E}\frac{V^{-1}(x)}{\sqrt{E-x}}$$ fro a some constant 'A' , then my question is since ...
741 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 ...
66 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 ...
271 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 ...
249 views

### Beyond WKB approximation for energies

In the first term the energies are given by the Wentzel–Kramers–Brillouin (WKB) formula $$\oint p dq = 2\pi \left( n+\frac{1}{2} \right)$$ However, can this formula be improved to include ...
174 views

### Hawking radiation for closely orbiting black holes

Suppose we have two black holes of radius $R_b$ orbiting at a distance $R_r$. I believe semi-classical approximations describe correctly the case where $R_r$ is much larger than the average black body ...
427 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 ...
289 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 ...
688 views

### exponential potential solution

let be the Schroedinguer equation $$- \frac{d^{2}}{dx^{2}}y(x)+ae^{cx}y(x)=E_{n}$$ (1) here a and c are constants. i know how to solve it from http://eqworld.ipmnet.ru/en/solutions/ode/ode0232....
436 views

Firstly, I'm aware that Hawking radiation can be derived in the "normal" way using the Bogoliubov transformation. However, I was intrigued by the heuristic explanation in terms of tunneling. The ...
109 views

### is Bohr-sommerfeld formula valid if the potential is non-smooth?

let be a non-smooth potential , for example a linear combination of step functions $$\sum_{n=0}^{10}H(x-n)$$ my question is, for this potential would be Bohr-sommerfeld quantization formula valid ?...
56 views

### Ground state energy $E_{0}$ and evaluation of physical energies

Given the lowest eigenvalue $E_0$ of an Schrödinguer operator, do the other energies $E_{n}$ for $n >0$ depend strongly on the lowest eigenvalue of the system? I mean, if we somehow fixed the ...
145 views

### What is the spectrum of energies for the potential $a^{x}$?

Given a certain potential $a^{x}$ with positive non-zero 'a' are there a discrete spectrum of energy state for the Schrodinger equation  \frac{- \hbar ^{2}}{2m} \frac{d^{2}}{dx^{2}}f(x)+a^{x}f(x)...
58 views

### Positive energies

If the potential is bounded below $V(x)=V(-x) \ge a$ for some real number $a$, and we can be sure that as $x\rightarrow \infty$ we know that $V(x) \ge 0$ then does it mean that the energies for ...
208 views

### can we apply WKB method for curved space times

let be the Hamiltonian of a surface $H= g_{a,b} p^{a}p^{b}$ (Einstein summation assumed) my question is if although the space time is curved then can we use the WKB approximation to get the quantum ...
2k 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 ...
116 views

### functional determinant evaluaton

given a Hamiltonian and the semiclassical WKB partition function in units $\hbar =2m=1$ $\Theta (t) = \frac{1}{2\pi} \iint dx dp exp(-tp^{2}-tV(x))$ can i use this Theta function to evaluate the ...
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 ...