WKB approximation

Often, this is approached through "quasi-classical" techniques (cf. WKB approximation).

One way to calculate this probability is by means of the semi-classical WKB approximation, which requires the value of to be small.

SUSY concepts have provided useful extensions to the WKB approximation.

This is found using the WKB approximation to match the ground state hydrogen wavefunction though the suppressed coulomb potential barrier.

When faced with such systems, one usually turns to other approximation schemes, such as the variational method and the WKB approximation.

But the difficulty with the WKB approximation is that this variable is described by the trajectory of the particle which, in general, is complicated.

(An application of the WKB approximation to the scattering of radio waves from the ionosphere.)

By such a changing of constant term in the effective potential, the results obtained by WKB approximation reproduces the exact spectrum for many potentials.

The Wigner-Kirkwood series is a semiclassical series with eigenvalues given exactly as for WKB approximation.

The early steps involved in the eikonal approximation in quantum mechanics are very closely related to the WKB approximation.

Making use of WKB approximation we can write the wave function of the scattered system in term of action S:

Usually, the WKB approximation for the tunneling current is used to interpret these measurements at low tip-sample bias relative to the tip and sample work functions.

A common semiclassical method is the so-called WKB approximation (also known as the "JWKB approximation").

The Langer correction is a correction when WKB approximation method is applied to three-dimensional problems with spherical symmetry.

Integrals with degenerate saddle points naturally appear in many applications including optical caustics and the multidimensional WKB approximation in quantum mechanics.

Problems in real life often do not have one, so "semiclassical" or "quasiclassical" methods have been developed to give approximate solutions to these problems, like the WKB approximation.

It appeared originally in the study of the WKB approximation and appears frequently in the study of quantization and in symplectic geometry and topology.

Although the tunneling transmission probability T is generally unknown, at a fixed location T increases smoothly and monotonically with the tip-sample bias in the WKB approximation.

In mathematical physics, the WKB approximation or WKB method is a method for finding approximate solutions to linear partial differential equations with spatially varying coefficients.

Less extreme approximations include, the WKB approximation, physical optics, the geometric theory of diffraction, the uniform theory of diffraction, and the physical theory of diffraction.

The WKB approximation describes the simplest picture of tunnelling in which the probability of barrier penetration is exponentially dependent on the product of the barrier height and thickness.

The condition for a reflection to occur as the atom experiences the attractive potential can be given by the presence of regions of space where the WKB approximation to the atomic wave-function breaks down.

The more basic of these include the method of matched asymptotic expansions and WKB approximation for spatial problems, and in time, the Poincaré-Lindstedt method, the method of multiple scales and periodic averaging.

Although the Schrödinger equation was developed two years later, Wentzel, Kramers, and Brillouin were apparently unaware of this earlier work, so Jeffreys is often neglected when credit is given for the WKB approximation.

In 1926, Wentzel, Hendrik Kramers, and Léon Brillouin independently developed what became known as the Wentzel-Kramers-Brillouin approximation, also known as the WKB approximation, classical approach, and phase integral method.