EXACT AND SEMICLASSICAL DENSITY-MATRIX OF A PARTICLE MOVING IN A BARRIER POTENTIAL WITH BOUND-STATES

We present a barrier potential with bound states that is exactly solva ble ansi determine the eigenfunctions and eigenvalues of the Hamiltoni an. The equilibrium density matrix of a particle moving at temperature T in this nonlinear barrier potential field is determined. The exact density matrix is compared with the result of the path integral approa ch in the semiclassical approximation. For opaque barriers the simple semiclassical approximation is found to be sufficient at high temperat ures while at low temperatures the fluctuation paths may have a causti c depending on temperature and endpoints. Near the caustics the diverg ence of the simple semiclassical approximation of the density matrix i s removed by a nonlinear fluctuation potential. For opaque barriers th e improved semiclassical approximation is again in agreement with the exact result. In particular, bound states and the form of resonance st ates are described accurately by the semiclassical approach. (C) 1996 American Institute of Physics.