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Results tagged with semiclassical
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user 66086
Semiclassical descriptions involve a base/background part described classically, and quantum parts representing an effective development in powers of Planck's constant, ħ. They cover systematic approximations such as the WKB, intuitive approaches to the correspondence limit, and a broad class of interstitial physical phenomena.
2
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The classical limit of quantum mechanics through Ehrenfest's theorem
The key point is that ℏ is dimensionful, with units of action (or angular momentum), and the classical limit is that in which the characteristic action quantities of the system are huge multiples of …
- 66.4k
4
votes
Negative probabilities with Wigner quasi-probability distributions
I'm not sure what you are getting wrong... Your expression, indeed, should go to 1 as β goes to 0. There must be some error in your implementation.
The Wigner transform of the canonical ensemble den …
- 66.4k
2
votes
The connection between classical phase space and quantum multiplicity
The standard intuitive path to the classical limit, or, conversely, to quantization, often goes through the phase space formulation of quantum mechanics.
The analog of the Liouville probability densit …
- 66.4k
1
vote
Klein-Gordon equation in the non-relativistic and semiclassical limit in a Wigner approach
Assuming you are considering the plane-wave solution of the K-G equation, take it to be in 1+1 for computational simplicity,
$$
\phi \propto \exp \left (-it\sqrt{k^2 + M^2c^2/\hbar^2} +ikx\right ),
…
- 66.4k
2
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Does the integral of a Wigner function over a finite region mean anything?
@Quantum Mechanic appears to have answered your question in his comments: of course conditioned (masked) quasiprobability distributions are meaningful, just as such probability distributions are meani …
- 66.4k
1
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Does quantum mechanics require classical mechanics for its own formulation?
I really don't understand the question, but I seldom do. QM "corrects" classical mechanics, stretching it like relativity, and includes it as a tricky "classical limit", but it crucially further inc …
- 66.4k
4
votes
Accepted
The question about commutator $[\hat{x},\hat{p}]=i\hbar$ at $\hbar\rightarrow 0$ seemingly c...
There is a systematic invertible change of language (Weyl correspondence) between Hilbert space operators and phase-space q-number variables,
$$
\hat A \leftrightarrow A, \qquad \hat B \leftrightarrow …
- 66.4k
2
votes
Accepted
Wigner Function and Spin in the Classical Limit?
You appear to have a vision I have not yet fathomed, so I would deny you the opportunity for confusion and consider just two bosons, nonrelativistically (which gets rid of the spin-statistics talk). Y …
- 66.4k
1
vote
Momentum operator generator of translation classical limit
You are willfully misunderstanding the $\hbar/S \to 0$ classical limit. ℏ is dimensionful, so choosing enormous units to measure it with, like MKSA units to measure moving trains, makes it look small. …
- 66.4k
2
votes
Wigner transform, convolution, and poles
I'll just jot down a few remarks and an unsatisfactory example that is easier to compute with; however, it is based on the "crypto-semiclassical" oscillator that most seasoned professionals appreciate …
- 66.4k
2
votes
Accepted
Intution for the physical meaning of high energy limit of a quantum states and uniform distr...
If, instead, you wished to persist in semiclassical wavefunctions, you might consider M V Berry (1981) "Quantizing a classically ergodic system: Sinai's billiard and the KKR method", Ann Phys 131 (1) …
- 66.4k
0
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Can I swap quantum mechanical ground state for some classical trajectory distribution and ha...
I am late in the discussion, and I've missed out on subtleties; but the way I might approach the problem would be through simple paradigms: well, the oscillator, is as classical as quantum systems go …
- 66.4k
12
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Accepted
Is the Moyal-Liouville equation $\frac{\partial \rho}{\partial t}= \frac{1}{i\hbar} [H\stack...
"Used in anger" or "killer ap"? To my knowledge, no problem has been solved in the phase-space quantization language that was not solvable in the other two formulations/pictures (Hilbert space or path …
- 66.4k
1
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"Deriving" Poisson bracket from commutator
The subleading terms, the terms that trouble you in the semiclassical approximation, are much easier in the deformation-quantization formulation. …
- 66.4k
4
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Classical limit of Moyal bracket in integral representation
There are no compact integral forms of the PBs, of course, unless you consider conversions of derivatives into powers of the Fourier conjugate variable, as you might be insinuating in the comments. T …
- 66.4k