Eigenvalue Problem for Schroedinger Operators and Time-Dependent Harmonic Oscillator

Details Eigenvalue Problem for Schroedinger Operators and Time-Dependent Harmonic Oscillator Eigenvalue Problem for Schroedinger Operators and Time-Dependent Harmonic Oscillator

1997-06-26

arxiv.org/abs/quant-ph/9706056v1

Physics

Quantum Physics

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It is shown that the eigenvalue problem for the Hamiltonians of the standard form, $H=p^2/(2m)+V(x)$, is equivalent to the classical dynamical equation for certain harmonic oscillators with time-dependent frequency. This is another indication of the central role played by time-dependent harmonic oscillators in quantum mechanics. The utility of the known results for eigenvalue problem in the solution of the dynamical equations of a class of time-dependent harmonic oscillators is also pointed out.

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