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.
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WKB Approximation of the Quasinormal Mode Spectrum of the Poschl-Teller (PT) Potential
In Black Hole Spectroscopy, it is well known that the Pöschl-Teller (PT) potential behaves approximately, or similarly to the more complicated Regge-Wheeler (RW) Potential.
The WKB Approximation has ...
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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-...
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How can we calculate simple quantum tunneling processes from the path integral?
I've been reading through Altland and Simons' Condensed Matter Field Theory, and am confused a bit by their discussion on tunneling and instantons. However I don't quite understand how this relates to ...
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dipole-radiation in semiclassical dynamics solid state
Using the semiclassical dynamics in solid state physics (electrons on a lattice with periodic potential, constrained to a band structure), we usually obtain that in the presence of external fields (...
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"Deriving" Poisson bracket from commutator
This Q/A shows that deriving P.B.s from commutators is subtle. Without going into deep deformation quantization stuff, Yaffe manages to show that $$\lim_{\hbar \to 0}\frac{i}{\hbar}[A,B](p,q)=\{a(p,q),...
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Why Normalise by $h$ in the Partition Function for Classical Harmonic Oscillator?
I was wondering if anyone could explain the reasoning behind the $h$ normalization constant when calculating the partition function for a classical harmonic oscillator.
I know that the partition ...
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Classical limits of Quantum Electrodynamics?
Quantum Electrodynamics is the theory that studies the interactions between matter and radiation (somewhat).
How would one explain for example the movement of an electron in a constant electric field ...
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Resource for WKB approximation formula
Is there any source that explicitly writes down the WKB "function" (to be defined soon) in orders of time derivative of the frequency over the frequency? Of course only to some finite order.
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What happens to branching in the Many-Worlds Interpretation of quantum mechanics in the limit when Planck's constant goes to 0?
We learn from quantum mechanics courses that one recovers classical mechanics in the limit when Planck's constant goes to zero. This can be seen in the path integral formulation. This is why ...
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Stimulated emission semiclassical model for atom recoil
In the context of Saturated absorption spectroscopy, I'm having trouble modeling stimulated emission, and getting the result that is written in articles, such as this article. I tried to use a non-...
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Making sense of stationary phase method for the path integral
I am trying to understand this paper/set of notes. I have already seen the following related question: Does the stationary phase approximation equal the tree-level term? but had some trouble following ...
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The question about commutator $[\hat{x},\hat{p}]=i\hbar$ at $\hbar\rightarrow 0$ seemingly can't match with Poisson bracket $\{x,\,p\}=1$ [duplicate]
At the limit $\hbar\rightarrow 0$, all "quantum" should tend to "classical", but why is the quantum commutator $[\hat{x},\hat{p}]=i\hbar$ at $\hbar\rightarrow 0$ equal to $0$, but ...
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Classical formulation of mechanics applied to Quantum Mechanics
According to Ehrenfest's theorem, the expectation values of observables such as position ($x$), momentum ($p$), etc. behave not only in a deterministic way but in fact in a classical way. Therefore, ...
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Semi-classical Quantum Ping-Pong in an infinite well potential
The general one particle state in a simple infinite well of size $L$ is a superposition of all the Hamiltonian eigen-states:
$$\tag{1}
\psi(x, t) = \sqrt{\frac{2}{L}} \sum_{n = 1}^{\infty} c_n \, e^{-\...
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Relation between the wavelength and the particle-wave duality
I will go straight into an example. Let's take the case of an electron of mass $m$ confined in an infinite 1D box of width $a$. Solving the Schrödinger equation and pay attention to the boundary ...
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