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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 ...
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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 ...
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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 $$ (n+1)2\pi \hbar ...
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14 views
could we obtain the potential (in one dimension) from the Gutzwiller trace?
to solve and obtain the potential of a 1-D Hamiltonian we must solve an integral equation
$$ N(E)= A \int_{0}^{E}\frac{V^{-1}(x)}{\sqrt{E-x}}$$
fro a some constant 'A' , then my question is since ...
1
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39 views
Length of the orbit (semiclassical orbits)
The Gutzwiller trace is about
$$ d(E)=d_{0} (E)+ \sum_{p.o}A_{p}Cos(S(E)l_{p}) $$
and $ l_{p} $ are the length of the orbit
However my question is, how can one derive the length of the orbit from ...
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63 views
functional determinant evaluaton
given a Hamiltonian and the semiclassical WKB partition function in units $ \hbar =2m=1 $
$ \Theta (t) = \frac{1}{2\pi} \iint dx dp exp(-tp^{2}-tV(x)) $
can i use this Theta function to evaluate the ...
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54 views
spectral eigenvalue staircase and quantum system
in a d-dimensional system of Quantum physics , does the Eigenvalue staircase
$ N(E)= \sum_{E_{n}\le E} 1 $ determine ALL the properties of Quantum System ??
for example, let us assume that the ...
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60 views
is there an error in this paper ¿¿
http://vixra.org/pdf/0908.0079v1.pdf
see equation (2.21) the reasoning to get this (2.21) goes from page 9 to page 14
should be the inverse of the potential denoted by $ x(V) $ proportional to the ...
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33 views
equation for the potential in terms of the phase shift for a rotational invariant potential
let be a potential in 3d invariant under rotations so $ V(r) $
in the WKB approximation the phase shifts are given by
$$ \delta _{l} (k)= \int_{a}^{\infty}dr ...
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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 $ ...
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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 ...
