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1
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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 ...
3
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2answers
176 views
Density of states via a Laplace transform
Is this formula correct?
$$ \frac{-1}{\pi}Im\int_{0}^{\infty}\!dt~\exp(Et)\Theta (t)\exp(i \epsilon t) ~=~ \sum _{n}\delta (E-E_{n}), $$
$$ \Theta (t)~=~ \sum_{n}\exp(-tE_{n}) ,$$
and I have used ...
0
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0answers
135 views
Bohr sommerfeld quantiztion rule and Gutzwiller trace
assuming we can evaluate the eigenvalue staircase $ N(E) $ in both manners with the Bohr-Sommerfeld quantization rule
$ N(E)2\pi \hbar = \oint _{C}p.dq $
and using the Gutzwiller trace $ N(E)= ...
1
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1answer
83 views
understanding the oscillating part of the Gutzwiller trace
given the density of states according to Gutzwiller's trace formula
$ g(E)= g_{smooth}(E)+ g_{osc}(E) $
i know that the 'smooth' part comes from $ g_{smooth}(E)= \iint dxdp \delta(E-p^{2}-V(x)) $ ...
