Eigenvalues and Eigenfunctions for the Harmonic Oscillator with Quartic, Sextic and Octic Perturbations

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This Demonstration calculates eigenvalues and eigenfunctions for the perturbed Schrödinger equation with , where . Units are . The energies and wavefunctions for the unperturbed potential are given by and , where is a Hermite polynomial. When you select "", the numerical solution for and the unperturbed solution are plotted. When you select "", is plotted. When you select "", is shown as a solid black line, as a dashed red curve and as a blue curve. The unperturbed eigenvalue is given by in all cases.

Contributed by: Santos Bravo Yuste (April 2019)
Open content licensed under CC BY-NC-SA



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