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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