๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

The general quantum-mechanical solution to the harmonic oscillator with a time-dependent force constant

โœ Scribed by C.J. Ballhausen


Publisher
Elsevier Science
Year
1991
Tongue
English
Weight
124 KB
Volume
178
Category
Article
ISSN
0009-2614

No coin nor oath required. For personal study only.

โœฆ 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.


๐Ÿ“œ SIMILAR VOLUMES


The dynamics of a harmonic oscillator wi
โœ Pranab Sarkar; Satrajit Adhikari; S.P. Bhattacharyya ๐Ÿ“‚ Article ๐Ÿ“… 1994 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 616 KB

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

Solutions to the time-dependent, forced
โœ I.L. Thomas ๐Ÿ“‚ Article ๐Ÿ“… 1980 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 427 KB

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 solution to a general quantum mech
โœ Rafael Almeida; Daniel A. Morales ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 140 KB ๐Ÿ‘ 3 views

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