Time Evolution of Quantum-Mechanical Harmonic Oscillator with Time-Dependent Frequency

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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

("Calculating ..." sometimes appears when the Demonstration cannot compute a solution.)


Contributed by: Michael Trott with permission of Springer. (March 2011)
From: The Mathematica GuideBook for Numerics, second edition by Michael Trott (© Springer, 2008).
Open content licensed under CC BY-NC-SA



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