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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.

356 questions
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Beyond WKB approximation for energies

In the first term the energies are given by the Wentzel–Kramers–Brillouin (WKB) formula $$ \oint p dq = 2\pi \left( n+\frac{1}{2} \right) $$ However, can this formula be improved to include further corrections? For example the wave function in the…
Jose Javier Garcia
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Ground state energy $ E_{0} $ and evaluation of physical energies

Given the lowest eigenvalue $E_0$ of an Schrödinguer operator, do the other energies $ E_{n} $ for $ n >0 $ depend strongly on the lowest eigenvalue of the system? I mean, if we somehow fixed the eigenvalue $E_{0}$, could we get more or at least…
Jose Javier Garcia
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Semiclassical vs classical

A system can only be called semiclassical if there are parts of the system that are described classically and parts decsribed quantum-mechanically. In this paradigm, physical quantites are described in a power series of $\hbar$, with the zero order…
nightmarish
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Why the proportionality factor of 'Quantum' Poisson brackets is imaginary?

When trying to understand the correspondence principle, I found a proof in this section (of this book) about why the quantum Poisson brackets ($\{\,,\,\}_{\text{QM}}$) must be proportional to the commutator ($[\,,\,]_{-}$). But, I'm stuck in the…
Gabriel Sandoval
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Transmission coefficient of second-order WKB approximation

In WKB approximation we expand the action in powers of $\hbar$ $$S(x)=S_0(x)+\dfrac{\hbar}{i}S_1(x)+\left(\dfrac{\hbar}{i}\right)^2S_2(x)+...$$ In standard treatment only terms up to and including $S_1(x)$ are used. In such a case, the transmission…
Omar Nagib
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is Bohr-sommerfeld formula valid if the potential is non-smooth?

let be a non-smooth potential , for example a linear combination of step functions $$ \sum_{n=0}^{10}H(x-n) $$ my question is, for this potential would be Bohr-sommerfeld quantization formula valid ?? is there any resource where they apply bohr…
Jose Javier Garcia
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bohr-sommerfeld quantiztion condition from semiclasical WKB

in WKB the quantization conditions are $$ \oint _{C} p.dq =2\pi n \hbar \tag{1}$$ and the wave function is $$ \Psi(x)= exp \left( \frac{iS[y(x)]}{\hbar} \right), \tag{2}$$ but what boundary conditions must I impose to this wave function if I want to…
Jose Javier Garcia
  • 4,719