ua nt - p h / 99 11 09 3 v 3 2 1 Ja n 20 02 SCHRÖDINGER EQUATIONS WITH TIME - DEPENDENT
نویسندگان
چکیده
We present some general results for the time-dependent mass Hamiltonian problem with H = − 2e∂xx + h(2)(t)e2ν(t)x2, where ν(t) is a continuous function of t. This Hamiltonian corresponds to a time-dependent mass (TM) Schrödinger equation with the restriction that there are only P 2 and X2 terms. We give the specific transformations to a different quadratic Schrödinger(TQ) equation and to a different time-dependent oscillator (TO) equation. For each Schrödinger system, we give the Lie algebra of space-time symmetries and (x, t) representations for number states, coherent states, and squeezed states. These general results include earlier work as special cases.
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