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25 views

semiclassical quantization failure

could exist 2 different Hamiltonians $ H1 $ and $ H2$ so a) The SEMICLASSICAL eigenvalue staircase is equal i mean the expression $$ \oint _{C} p.dq = n+\alpha $$ but the real eigenvalues $ E_{n} ...
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0answers
22 views

WKB transmission probability in momentum space

What is the expression for the WKB transmission probability in momentum space?
6
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3answers
167 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 ...
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1answer
41 views

Vacuum energy: black hole evaporation and cosmology - a discrepancy?

Black hole evaporation is a result of calculating the expectation value of the stress-energy tensor of the state of the vacuum in certain spacetimes and then making a plausibility argument as to the ...
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1answer
162 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 ...
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1answer
331 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 < ...
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1answer
109 views

Semiclassical Approximation

In many books I read about semiclassical approximation applied to the field of Bose-Einstein condensation. But I don't understand what it really means. For example I read that an expression like this ...
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1answer
102 views

Semiclassical description of EM waves reflection from metallic surfaces

Imagine an EM wave impinging on a metal. Fresnel's formulas tell us that no wave can propagate through the metal, or that the transmitted field is an evascent wave with some penetration depth ...
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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 ...
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79 views

Spaans, “On Quantum Contributions to Black Hole Growth”

This paper was posted to arxiv a couple of weeks ago: http://arxiv.org/abs/1309.1067 From the abstract: The effects of Wheeler's quantum foam on black hole growth are explored from an ...
4
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1answer
374 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
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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 ...
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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 ...
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0answers
85 views

WKB expression for Dirac equation?

given the one dimensional Schroedinger equation $$ - \frac{\hbar ^{2}}{2m} \frac{d^{2}}{dx^{2}}\Psi(x)+ V(x) \Psi(x) =E_{n}\Psi (x) $$ the WKB method for the energies is $$ (n+1)2\pi \hbar ...
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0answers
62 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 ...
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0answers
16 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 ...
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1answer
439 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 ...
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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 ...
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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 ...
7
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1answer
164 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 ...
7
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0answers
109 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 ...
3
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1answer
239 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 ...
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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 ...
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1answer
317 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 ...
9
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1answer
187 views

Hawking Radiation as Tunneling

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 ...
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1answer
83 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 ...
2
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1answer
54 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 ...
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2answers
120 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} ...
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0answers
43 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 ...
2
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2answers
167 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 ...
6
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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 ...
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0answers
79 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 ...
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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 ...