Hermite polynomials are a set of orthogonal polynomials that arise in probability theory, combinatorics, and physics, especially in the context of the quantum harmonic oscillator. These polynomials provide a mathematical framework for describing the wavefunctions of the quantum harmonic oscillator, which describes a particle bound in a potential well. The eigenstates of the quantum harmonic oscillator are represented by these polynomials, and they play a crucial role in determining the energy levels of the system.
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