The semiclassical tag has no wiki summary.
8
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1answer
86 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
1answer
207 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 ...
6
votes
0answers
87 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 ...
5
votes
3answers
446 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 ...
5
votes
1answer
92 views
Beyond WKB approximation for energies
at first term the energies are given by the WKB formula
$$ \oint p.dq = 2\pi (n+1/2) $$
however can this formula be improved to include further corrections ??,
for example the wave function in the ...
4
votes
1answer
130 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 ...
4
votes
0answers
101 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
134 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
142 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
224 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 ...
2
votes
1answer
51 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
125 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 ...
1
vote
2answers
87 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
$$ \frac{- \hbar ^{2}}{2m} ...
1
vote
1answer
159 views
exponential potential solution
let be the Schroedinguer equation
$$ - \frac{d^{2}}{dx^{2}}y(x)+ae^{cx}y(x)=E_{n} $$ (1)
here a and c are constants.
i know how to solve it from ...
1
vote
1answer
57 views
is Bohr-sommerfeld formula valid if the potential is non-smooth?
let be a non-smooth potential , for example a linear combination of step functions
$$ \sum_{n=0}^{10}H(x-n) $$
my question is, for this potential would be Bohr-sommerfeld quantization formula valid ...
1
vote
0answers
52 views
WKB expression for Dirac equation?
given the one dimensional Schroedinger equation
$$ - \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
0answers
14 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
39 views
Length of the orbit (semiclassical orbits)
The Gutzwiller trace is about
$$ d(E)=d_{0} (E)+ \sum_{p.o}A_{p}Cos(S(E)l_{p}) $$
and $ l_{p} $ are the length of the orbit
However my question is, how can one derive the length of the orbit from ...
1
vote
0answers
63 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
54 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
60 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
31 views
equation for the potential in terms of the phase shift for a rotational invariant potential
let be a potential in 3d invariant under rotations so $ V(r) $
in the WKB approximation the phase shifts are given by
$$ \delta _{l} (k)= \int_{a}^{\infty}dr ...
0
votes
0answers
21 views
Gutzwiller series cuestion about the sum over orbits
since the sum of the periodic orbit in the Gutzwiller series is DIVERGENT
$$ \sum_{p.p.o}A_{p}Cos(S(l(p)/ \hbar+\mu _{p}) $$
cna we simply 'truncate' it i mean you take only the first $ 1000 $ ...
0
votes
0answers
39 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 ...
