What is associated Laguerre polynomial?

What is associated Laguerre polynomial?

The Laguerre polynomials arise in quantum mechanics, in the radial part of the solution of the Schrödinger equation for a one-electron atom. They also describe the static Wigner functions of oscillator systems in quantum mechanics in phase space.

What is generating function for Laguerre polynomials?

n ! L n α ( x ) = ( α + 1 ) n F 1 1 ( − n ; α + 1 ; x ) and the generating function is. ∑ n = 0 ∞ L n α ( x ) t n = ( 1 − t ) − α − 1 exp ( x t t − 1 ) Laguerre polynomials occur as eigenfunctions of the hydrogen atom.

Which of the following is chebyshev differential equation?

Chebyshev’s differential equation is (1 − x2)y′′ − xy′ + α2y = 0, where α is a constant.

Why do we need Hermite polynomials?

Hermite polynomials are relevant for the analysis of the quantum harmonic oscillator, and the lowering and raising operators there correspond to creation and annihilation.

What is Hermite polynomial equation?

Hermite Polynomials ( n − 2 k ) ! Their generating function is. ∑ n = 0 ∞ H n ( x ) t n n ! = exp ( 2 x t − t 2 ) Hermite polynomials are relevant for the analysis of the quantum harmonic oscillator, and the lowering and raising operators there correspond to creation and annihilation.

What are Chebyshev polynomials used for?

The Chebyshev polynomials are used for the design of filters. They can be obtained by plotting two cosines functions as they change with time t, one of fix frequency and the other with increasing frequency: ⁡ ( 2 π t ) , y ( t ) = cos ⁡

What is Chebyshev method?

In numerical linear algebra, the Chebyshev iteration is an iterative method for determining the solutions of a system of linear equations. The method is named after Russian mathematician Pafnuty Chebyshev. Chebyshev iteration avoids the computation of inner products as is necessary for the other nonstationary methods.