Time-dependent raising and lowering operators for the ageing, forced and damped oscillator in quantum mechanics
✍ Scribed by C.J. Ballhausen
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 352 KB
- Volume
- 192
- Category
- Article
- ISSN
- 0009-2614
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✦ Synopsis
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 adjoint 6+(x, p, t) be zero makes these the lowering and raising operators for a set of eigenvectors to the dynamic harmonic oscillators. The lowest eigenvector can therefore be constructed solving a first-order differential equation in a/ax, whereafter a complete set can be generated by the application of d+(x, p, t). The functional time dependence of h( t) and dt (t) is simply given as the solution to Newton's second law of motion.