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Questions tagged [semiclassical]

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.

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.

380 questions
62
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3 answers

How is the Saddle point approximation used in physics?

I am trying to understand the saddle point approximation and apply it to a problem I have but the treatments I have seen online are all very mathematical and are not giving me a good qualitative description of the method and why it's used and for…
BeauGeste
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60
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6 answers

Tree-level QFT and classical fields/particles

It is well known that scattering cross-sections computed at tree level correspond to cross-sections in the classical theory. For example the tree-level cross-section for electron-electron scattering in QED corresponds to scattering of classical…
Squark
39
votes
7 answers

Do Maxwell's equation describe a single photon or an infinite number of photons?

The paper Gloge, Marcuse 1969: Formal Quantum Theory of Light Rays starts with the sentence Maxwell's theory can be considered as the quantum theory of a single photon and geometrical optics as the classical mechanics of this photon. That…
asmaier
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38
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7 answers

Does spin really have no classical analogue?

It is often stated that the property of spin is purely quantum mechanical and that there is no classical analog. To my mind, I would assume that this means that the classical $\hbar\rightarrow 0$ limit vanishes for any spin-observable. However, I…
Akoben
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25
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1 answer

How is the logarithmic correction to the entropy of a non-extremal black hole derived?

I`ve just read, that for non-extremal black holes, there exists a logarithmic (and other) correction(s) to the well known term proportional to the area of the horizon such that $$S = \frac{A}{4G} + K \ln \left(\frac{A}{4G}\right)$$ where $K$ is a…
Dilaton
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23
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9 answers

Why did the Bohr Model Successfully calculate some of the energy levels in hydrogen?

The Bohr model is incomplete and has drawbacks. But one thing is a mystery to me. Why did it so successfully calculate the Rydberg series with quite good number of correct digits? Having such a good prediction one would expect that there exists an…
Stefan
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22
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5 answers

Why does electron orbital circumference have to be in multiples of de Broglie wavelengths?

Electron orbit circumferences have to be in multiples of its de Broglie wavelength, but what do those 2 have in common?
radial9174
  • 551
20
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2 answers

Semiclassical limit of Quantum Mechanics

I find myself often puzzled with the different definitions one gives to "semiclassical limits" in the context of quantum mechanics, in other words limits that eventually turn quantum mechanics into classical mechanics. In a hand-wavy…
Ellie
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3 answers

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 with something like the WKB-wavefunction and shortly…
user9886
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18
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3 answers

Is there a second-order non-linear addition to Maxwell's equations?

Maxwell's equations are famously linear and are the classical limit of QED. The thing is QED even without charged particles is pretty non-linear with photon-photon interaction terms. Can these photon-photon interaction terms have a "classical" limit…
Aravind Karthigeyan
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18
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1 answer

On Groenewold's Theorem and Classical and Quantum Hamiltonians

I recently encountered Groenewold's Theorem or the Groenewold-Van Hove Theorem which shows that there is no function which can satisfy the following mapping $$ \{A,B\} \to \frac{1}{i\hbar}[A,B].$$ Does this show that there exist Quantum Hamiltonians…
Jake Xuereb
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5 answers

Is the Moyal-Liouville equation $\frac{\partial \rho}{\partial t}= \frac{1}{i\hbar} [H\stackrel{\star}{,}\rho]$ used in applications?

This answer by Qmechanic shows that the classical Liouville equation can be extended to quantum mechanics by the use of Moyal star products, where it takes the form $$ \frac{\partial \rho}{\partial t}~=~ \frac{1}{i\hbar}…
Emilio Pisanty
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18
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5 answers

Can I swap quantum mechanical ground state for some classical trajectory distribution and have it sit still after the swap?

Suppose that I have a single massive quantum mechanical particle in $d$ dimensions ($1\leq d\leq3$), under the action of a well-behaved potential $V(\mathbf r)$, and that I let it settle on the ground state $|\psi_0⟩$ of its…
Emilio Pisanty
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17
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8 answers

How can Planck's constant take different values?

I have seen books and papers mentioning "In the semiclassical limit, $\hbar$ tends to zero", "the scaled Planck's constant goes as $1/N$ where $N$ is the Hilbert space dimension" etc. Could anyone explain these variable values taken by Planck's…
Raman
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17
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1 answer

Bohr-Sommerfeld quantization condition from the WKB approximation

How can one prove the Bohr-Sommerfeld quantization condition $$ \oint p~dq ~=~2\pi n \hbar $$ from the WKB ansatz solution $$\Psi(x)~=~e^{iS(x)/ \hbar}$$ for the Schroedinger equation? With $S$ the Hamilton's principal function of the particle…
Jose Javier Garcia
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