A harmonic oscillator with time-dependent force constant when perturbed by a weak static quartic anharmonicity ti4, 1 small, is shown to generate new features in the dynamics. For weak coupling, both time-dependent perturbation theoretical analysis and near-exact numerical calculations predict that
The general quantum-mechanical solution to the harmonic oscillator with a time-dependent force constant
โ Scribed by C.J. Ballhausen
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 124 KB
- Volume
- 178
- Category
- Article
- ISSN
- 0009-2614
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โฆ Synopsis
The solution to Newton's second law for a harmonic oscillator with a time-dependent force constant allows the solutions to the corresponding time-dependent Schkidinger equation to be written down by analogy.
๐ SIMILAR VOLUMES
Tlme-dcpendent creation and annlhllatlon operators are derived which are used to obtam exact solutrons, in the coordinate representation, to the time-dependent, forced quantum oscillator equatron. The solutlons are used to obtain a general formula for the transItIon probablties, vahd for any tune-de
Exact analytical solutions are found for the quantum mechanical problem of a particle subject to a time-dependent potential with time-dependent boundary conditions. The method of solution employs time-dependent invariants, rescaling of space and time variables along with an unitary transformation. S