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.
Solutions to the time-dependent, forced quantum oscillator equation in the coordinate representation
โ Scribed by I.L. Thomas
- Publisher
- Elsevier Science
- Year
- 1980
- Tongue
- English
- Weight
- 427 KB
- Volume
- 70
- Category
- Article
- ISSN
- 0009-2614
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โฆ Synopsis
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-dependent force.
๐ SIMILAR VOLUMES
Raising and loweringoperators are constructed for the harmonic oscillator with a time-dependent force constant and for the damped and linearly forced oscillator. The demand that the total derivative [ ri(x, p, t), I?] +ifi a/at ri(x, p, t) of the time-dependent operator 6(x, p, t) and its Hermitian
explicit and local. Its novel features include the exact evaluation of a major contribution to an approximation to the The matrix elements of the exponential of a finite difference realization of the one-dimensional Laplacian are found exactly. This evolution operator (Eq. ( )) and a first-order ap
A numerical Fourier transform method is developed to solve the time-dependent Schrodinger equation in spherical coordinates. The method is tested for the rigid rotor and a model bending potential. Results are in excellent agreement with exact values.