Solutions

Try different values of n. The polynomial LegendreP[n,x] is an n:th degree polynomial with all its zeros on the interval [-1,1]. You will encounter these functions in quantum mechanics, where they constitute the solution for the angular part of the Hydrogen atom Schrödinger equation.

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Hermite polynomials, which form the solution for the wave function of the harmonic oscillator in quantum mechanics, are also n:th degree.

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Laguerre polynomials solve the radial part of the Hydrogen atom Schrödinger equation.

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Mathieu functions are needed in the theory of oscillators. Maybe you'll avoid these.

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The Riemann zeta-function is an important function in mathematics, but rarely needed in physics.

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Created by Mathematica  (April 10, 2007)