Electrostatic-field-induced dynamics in an ultrathin quantum well

We consider the time evolution of a particle subjected to both a uniform electrostatic field F and a one-dimensional delta-function potential well. We derive the propagator K_F(x,t|x’,0) of this system, directly leading to the wavefunction psi_F(x,t), in which its essential ingredient K_F(0,t|0,0), accounting for the ionization-recombination in the bound-continuum transition, is exactly expressed in terms of the multiple hypergeometric functions F(z_1,z_2,…,z_n). And then we obtain the ingredient K_F(0,t|0,0) in an appropriate approximation scheme, expressed in terms of the generalized hypergeometric functions p_F_q(z) being much more transparent to physically interpret and much more accessible in their numerical evaluation than the functions F(z_1,z_2,…,z_n).