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In this chapter, we will discuss the Hermite polynomials, named after Charles Hermite, (1822–1901). Hermite polynomials or functions are of interest in quantum mechanics, where they arise as solutions of the harmonic oscillator eigenvalue problem, or when we analyze the motion of a particle bound in a potential well. The Hermite polynomials also arise naturally as the modes of propagation in parabolic index optical waveguides.
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