The quantization tag has no wiki summary.
3
votes
1answer
57 views
Bohr-sommerfeld quatnization from the WKB approximation
how can one prove the Bohr Sommerfeld quantization formula
$$ \oint p.dq =2\pi n $$
from the WKB ansatz solution for the Schroedinger equation ?? $ \Psi(x)=e^{iS(x)/ \hbar} $
with $ S $ the action ...
7
votes
0answers
133 views
Magnetic monopole and electromagnetic field quantization procedure
From the Maxwell's equations point of view, existence of magnetic monopole leads to unsuitability of the introduction of vector potential as $\vec B = \operatorname{rot}\vec A$. As a result, it was ...
6
votes
0answers
224 views
exponential potential $ \exp(|x|) $
For $a$ being positive what are the quantization conditions for an exponential potential?
$$ - \frac{d^{2}}{dx^{2}}y(x)+ ae^{|x|}y(x)=E_{n}y(x) $$
with boundary conditions $$ y(0)=0=y(\infty) $$
I ...
6
votes
0answers
46 views
Pohlmeyer reduction of string theory for flat and AdS spaces
The definition of Pohlmeyer invariants in flat-space (as per eq-2.16 in Urs Schreiber's DDF and Pohlmeyer invariants of (super)string) is the following:
$ Z^{\mu_1...\mu_N} (\mathcal{P}) = ...
5
votes
0answers
78 views
Do semiclassical GR and charge quantisation imply magnetic monopoles?
Assuming charge quantisation and semiclassical gravity, would the absence of magnetically charged black holes lead to a violation of locality, or some other inconsistency? If so, how?
(I am not ...
5
votes
0answers
136 views
When can photon field amplitudes be written as field operators?
Suppose I have some classical field equation for two photon fields with amplitudes $A_1(z),A_2(z)$ (plane waves) given as
${A}_1=\alpha f(A_1,A_2) \\
{{A}_2}=\beta g(A_1,A_2) $
Under what ...
3
votes
0answers
71 views
Pohlmeyer reduction of string theory for flat- and AdS- spaces
The definition of Pohlmeyer invariants in flat-space (as per eq-2.16 in Urs Schreiber's DDF and Pohlmeyer invariants of (super)string) is the following:
$ Z^{\mu_1...\mu_N} (\mathcal{P}) = ...
2
votes
0answers
100 views
Quantization and natural boundary conditions
The Euler-Lagrange equations follow from minimizing the action. Usually this is done with fixed (e.g. vanishing) boundary conditions such that we do not have to worry about any boundary terms. ...
1
vote
0answers
63 views
Geometric quantization of a hydrogen atom
I want to know how to quantize a hydrogen atom as an example of geometric quantization. Apparently there is a derivation in the book "Geometric Quantization in Action: Applications of Harmonic ...
1
vote
0answers
69 views
shouldn't we add the oscillating terms into Bohr-Sommerfeld quantization formula
shouldn't be the quantization formula (in one dimension) equal to
$ N_{smooth}(E)+N_{osc}(E) = \oint_{C}p.dq $ ??
where the Oscillating term is just the correction from Gutzwiller trace formula or a ...
0
votes
0answers
17 views
Allowed Quantum States- Filkelstein and Rubinstein constraints
So basically i'm doing a report on Finkelstein and Rubinstein constraints. I have a system where the allowed quantum states satisfy ...
0
votes
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)= ...
