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7
votes
1answer
247 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 ...
8
votes
1answer
173 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 ...
4
votes
1answer
414 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
285 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 ...
1
vote
1answer
671 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 ...
11
votes
1answer
420 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 ...
1
vote
1answer
107 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
votes
1answer
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 ...
1
vote
2answers
144 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} ...
0
votes
0answers
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 ...
2
votes
2answers
207 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 ...
8
votes
3answers
1k 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
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 ...
1
vote
0answers
77 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 ...
16
votes
1answer
436 views

How is the logarithmic correction to the entropy of a non extremal black hole derived?

I`ve just read, that for non extremal black holes, there exists a logarithmic (and other) correction(s) to the well known term proportional to the area of the horizon such that $S = \frac{A}{4G} + K ...