The harmonic oscillator, described by the Schrödinger equation
is a central textbook example in quantum mechanics. Its time evolution can be easily given in closed form. More generally, the time evolution of a harmonic oscillator with a time-dependent frequency
can also be given in quadratures. This allows the efficient solution of the Schrödinger equation as a system of just three coupled nonlinear ordinary differential equations.
This Demonstration lets you see
and
for various time-dependent frequencies of the functional form
using the initial wave function (moving harmonic oscillator ground state)
.
("Calculating ..." sometimes appears when the Demonstration cannot compute a solution.)
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