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Solutions to explicit time-dependent Hamiltonians are rare. Specific propagators are known only for Hamiltonians that are quadratic in position and momentum, or that possess an additional invariant which allows to map the time-dependent problem to a related stationary problem.
Especially the description of decaying (or metastable) states requires the analysis of non-stationary systems. We analyzed the survival rate of states in a model, where we lower a barrier that confined the particle for t<0. These models are related to the Moshinsky shutter, which is a prime example for transient effects in the time-evolution of a quantum state. |
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