Quantum Tunneling in Time‐Dependent Potential Barrier: a General Formulation and Some Exactly Solvable Models

Quantum tunneling in one spatial dimension in the presence of time‐dependent potentials is investigated theoretically. First, a general multichannel formulation of the problem is given for harmonic time‐dependence. The case of an oscillatory delta‐function potential of constant strength is discussed at length and specific numerical calculations are presented for the reflection and transmission coefficients. Then other exactly solvable time‐dependent potentials are obtained by carrying out successive unitary transformations. As an example of this class, a delta‐function potential with time‐dependent strength and boundary conditions is studied. Finally tunneling time‐delay for time‐dependent potentials is formulated in the multichannel situation, and also the concept of first passage time for the decay of a wave packet confined to one well of a double well potential is generalized for the case of time‐dependent barrier and boundary conditions.