What is validity of WKB approximation?
The WKB approximation in calculating the asymptotic QNM frequency is always valid for the first and second category and it is always invalid for the third category .
What is connection formula in WKB approximation?
Semiclassical Analysis of a Particle Trapped in a Well in One Dimension. The WKB semiclassical approximate solution to Schrödinger’s equation, ψ(x)=ψ(x0)√p(x0)p(x)exp(±iℏ∫xx0p(x′)dx′)
What is slowly varying potential?
Consider a particle moving along in a slowly varying one-dimensional potential. By “slowly varying” we mean here that in any small region the wave function is well approximated by a plane wave, and that the wavelength only changes over distances long compared with a wavelength.
What is semiclassical approximation?
An approximation technique used to calculate quantities in quantum mechanics. This technique is called the semiclassical approximation because the wave function is written as an asymptotic series with ascending powers of the Planck constant, h, with the first term being purely classical.