Hermite polynomials in Quantum Harmonic Oscillator

Hermite polynomials in Quantum HarmonicOscillatorChristos T. AravanisChristos T. Aravanisis a senior majoring inMathematics and Theoretical Physics at the Uni-versity of Athens, graduation heplans to attend graduate school where he will studyMathematics. The content of this article reflects hisinterest in the applications of Mathematics to Quantum mechanics and in other branches of physics, it is common to ap-proach physical problems using algebraic and analytic methods. Examplesinclude the use of differential equations for many interesting models, the use ofquantum groups in Quantum physics, and of differential geometry in relativitytheory. In this article, we discuss the Hermite polynomials , some of their prop-erties and a brief description of their applications to the Quantum PolynomialsHermite polynomials , named after the French mathematician Charles Hermite ,are orthogonal polynomials , in a sense to be described below, of the formHn(x) = ( 1)nex2dndxne x2(1)forn= 0,1,2,3.

Hermite polynomials in Quantum Harmonic Oscillator Christos T. Aravanis Christos T. Aravanis is a senior majoring in Mathematics and Theoretical Physics at the Uni-

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