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9
votes
1answer
217 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 ...
7
votes
3answers
867 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 ...
7
votes
1answer
240 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
votes
1answer
183 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
votes
0answers
119 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 ...
6
votes
3answers
295 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 ...
6
votes
0answers
144 views

Eikonal approximation in QFT

Does the eikonal approximation for calculating a scattering amplitude in QFT provide the exact result in the limit of $s\rightarrow\infty$ at finite $t=0$ ($s$ and $t$ are the usual Mandelstam ...
5
votes
1answer
450 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
1answer
193 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 ...
5
votes
0answers
139 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 ...
4
votes
1answer
42 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 ...
4
votes
0answers
89 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 ...
3
votes
1answer
576 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
265 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 ...
3
votes
1answer
550 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 ...
2
votes
1answer
73 views

Is Ehrenfest theorem equivalent to Bohr's Correspondence Principle?

Ehrenfest theorem is usually dubbed as the quantum mechanical equivalent of Newton's law and Griffiths states, in the first chapter of his textbook, that Ehrenfests theorem enables us to work with ...
2
votes
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 ...
2
votes
2answers
179 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 ...
2
votes
1answer
43 views

Is WKB really applicable for the ground state?

It is a long time question for me. For me, it seems that WKB is applicable for a given $E$ if and only if $\hbar$ is sufficiently small. Or in other words, WKB is applicable if and only if the ...
2
votes
0answers
94 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 ...
1
vote
2answers
123 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} ...
1
vote
1answer
67 views

Is Gravitational Red shift equal to $mgh$

Is gravitational shift - $\frac{gh}{c^2}$ (according to pound-rebka experiment) always equal to $PE=mgh$? because assume the gravitational pull, $g$, is equal to $1$ then we can say $g = 1$ similarly ...
1
vote
2answers
164 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 ...
1
vote
2answers
70 views

Phase space derivation of quantum harmonic oscillator partition function

I would like to derive the partition function for the quantum Harmonic oscillator from scratch: $$\tag{1} Z = \int dp \, dx\, e^{-\beta H}.$$ The free particle appears in many textbooks. $H = ...
1
vote
1answer
260 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
517 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
1answer
145 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 ...
1
vote
1answer
354 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 ...
1
vote
1answer
87 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 ...
1
vote
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 ...
1
vote
0answers
56 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 ...
1
vote
0answers
92 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 ...
1
vote
0answers
65 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 ...
0
votes
0answers
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} ...
0
votes
0answers
30 views

WKB transmission probability in momentum space

What is the expression for the WKB transmission probability in momentum space?
0
votes
1answer
125 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 ...
0
votes
0answers
63 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 ...
0
votes
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 ...