Physics – Quantum Physics
Scientific paper
1999-11-20
Ann. Phys. 292 (2001) 23
Physics
Quantum Physics
LaTeX, 26 pages, including 3 figures and 13 tables. New title and format for journal. Conclusion added
Scientific paper
10.1006/aphy.2001.6145
We attack the specific time-dependent Hamiltonian problem H=-{1/2} (t_o/t)^a \partial_{xx} + (1/2) \omega^2 (t/t_o)^b x^2. This corresponds to a time-dependent mass (TM) Schr\"odinger equation. We give the specific transformations to a different time-dependent quadratic Schr\"odinger equations (TQ) and to a different time-dependent oscillator (TO) equation. For each Schr\"odinger system, we give the Lie algebra of space-time symmetries, the number states, the squeezed-state (with their classical motion), (\Delta x)^2, (\Delta p)^2, and the uncertainty product.
Nieto Michael Martin
Truax Rodney D.
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