Semiclassical coherent-state propagator via path integrals with intermediate states of variable width
- Instituto de Fisica 'Gleb Wataghin', Universidade Estadual de Campinas (UNICAMP), Caixa Postal 6165, 13083-970 Campinas (Brazil)
We derive a semiclassical approximation for the coherent state propagator <z{sup ''} vertical bar e{sup -iHt/({Dirac_h}/2{pi})} vertical bar z{sup '}> using a path integral formulation in which the intermediate coherent states can have arbitrary widths. Our semiclassical formula involves complex trajectories of the smoothed Hamiltonian H(q,p,b)=<z vertical bar H vertical bar z> where b, the width of the coherent state vertical bar z>, is a free function that can be chosen conveniently. The generality of this formalism enables us to derive a semiclassical approximation which contains, as particular cases, other similar approximations known in the literature, providing a natural link between them. We present numerical results showing that the semiclassical propagation can be very sensitive to the choice of b and we suggest an energy dependent value b=b{sub E} that results in considerable improvement over other choices. This value for the width will be generally different from the widths {sigma}{sup '} or {sigma}{sup ''} of the initial and final states vertical ba z{sup '}> and vertical bar z{sup ''}>.
- OSTI ID:
- 20640451
- Journal Information:
- Physical Review. A, Vol. 68, Issue 6; Other Information: DOI: 10.1103/PhysRevA.68.062112; (c) 2003 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
Similar Records
A semiclassical correction for quantum mechanical energy levels
Generalization of the coherent-state path integrals and systematic derivation of semiclassical propagators