Math 2.0

Special functions Orthogonal polynomials Concept

Hermite functions

Summary

The Hermite functions ψn\psi_n are the Hermite polynomials multiplied by the Gaussian e−x2/2e^{-x^2/2} and normalised. They form an orthonormal basis of the Hilbert space L2(ℝ)L^2(\R). Each ψn\psi_n is an eigenfunction of the Fourier transform and of the quantum harmonic oscillator.

Where this leads

3 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Hermite_polynomials
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MSC33C45, 42C10, 81Q05

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