Abstract
We review and discuss exact solutions for selected initial value problems. Starting with simple oscillator problems (forced harmonic oscillator, tunneling through a parabolic barrier, frequency modulated oscillator, Heisenberg microscope), we continue by reviewing various techniques which can be used to calculate propagators. We are then in a position to discuss analytic properties of problems which lie at the heart of quantum mechanics: Time-dependent field emission, exponential decay, the dynamics of resonant tunneling and the transfer of charge in atomic collisions. Special attention is paid to the evaluation and illustration of problems in terms of their analytic solutions.
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