SUSY concepts have provided useful extensions to the WKB approximation.

Green's work on the motion of waves in a canal anticipates the WKB approximation of quantum mechanics, while his research on light-waves and the properties of the ether produced what is now known as the Cauchy-Green tensor.

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

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

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

WKB approximation ).

* WKB approximation

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.

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.

:- WKB approximation: electrons in classical external electro-magnetic fields

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.

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

# REDIRECT WKB approximation

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 credit for the WKB approximation.

* WKB approximation

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.

In 1926, Gregor Wentzel, Hendrik Kramers, and Brillouin independently developed what is known as the Wentzel – Kramers – Brillouin approximation, also known as the WKB method, classical approach, and phase integral method.

* WKB approximation

For higher bias voltages, the predictions of simple planar tunneling models using the Wentzel-Kramers Brillouin ( WKB ) approximation are useful.

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.

The derivative of equation ( 5 ), I in the WKB approximation, is

The analysis of differential equations of such systems is often done approximately, using the WKB method ( also known as the Liouville – Green method ).

In a nonuniform medium, in which the wavenumber k can depend on the location as well as the frequency, the phase term kx is typically replaced by the integral of k ( x ) dx, according to the WKB method.

Generally, WKB theory is a method for approximating the solution of a differential equation whose highest derivative is multiplied by a small parameter ε.

WKB theory is a special case of multiple scale analysis.

Therefore the smallest error achieved by the WKB method is at best of the order of the last included term.

In the WKB theory, the tunneling current is predicted to be

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.

Very frequently it is calculated by using the Wentzel-Kramers-Brillouin ( WKB ) approximation.

For the same reason, it also serves to provide uniform semiclassical approximations near a turning point in the WKB method, when the potential may be locally approximated by a linear function of position.

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 measured brightness temperature is a good approximation to the brightness temperature at the center of the lunar disk because of the narrow antenna beam and because the temperature distribution over the central portion of the moon's disk is nearly uniform.

Although we are still far from a complete understanding of these problems, as a first approximation, it is suggested that alterations in the hypothalamic balance with consequent changes in the hypothalamic-cortical discharges account for major changes in behavior seen in various moods and states of emotions in man and beast under physiological circumstances, in experimental and clinical neurosis, and as the result of psychopharmacological agents.

This reduces to the relationship: Af, where Af is the intercept at zero thickness of the extrapolation of the slope indicated in eqn. ( 1 ), Af is the thickness of the coating equivalent to the rounding off of the knife tip, Af is a straight line first approximation of this roundness, and the other symbols are equivalent to those of eqn. ( 1 ).

The luminous gain of a single stage with Af ( flux gain ) is, to a first approximation, given by the product of the photocathode sensitivity S ( amp / lumen ), the anode potential V ( volts ), and the phosphor conversion efficiency P ( lumen/watt ).

In practice, a bidirectional reflectance distribution function ( BRDF ) may be required to characterize the scattering properties of a surface accurately, although the albedo is a very useful first approximation.

To test the hypothesis that all treatments have exactly the same effect, the F-test's p-values closely approximate the permutation test's p-values: The approximation is particularly close when the design is balanced.

In this model the electron cloud of a multi-electron atom may be seen as being built up ( in approximation ) in an electron configuration that is a product of simpler hydrogen-like atomic orbitals.

Fundamentally, an atomic orbital is a one-electron wave function, even though most electrons do not exist in one-electron atoms, and so the one-electron view is an approximation.

When thinking about orbitals, we are often given an orbital vision which ( even if it is not spelled out ) is heavily influenced by this Hartree – Fock approximation, which is one way to reduce the complexities of molecular orbital theory.

For much more distant objects the Euclidean approximation is not valid, and General Relativity must be taken into account when calculating the luminosity distance of an object.

BCS is able to give an approximation for the quantum-mechanical many-body state of the

This is because Brownian motion, whose time derivative is everywhere infinite, is an idealised approximation to actual random physical processes, which always have a finite time scale.

The bilinear transform is a first-order approximation of the natural logarithm function that is an exact mapping of the z-plane to the s-plane.

The inverse of this mapping ( and its first-order bilinear approximation ) is

It has efficient approximation algorithms, but is NP-hard to solve exactly.