The Asymptotic Behavior of the Wave Function for a Quasi-Stationary State

Marshall A. Bowen, Joseph Coster

Qian Shang-Wu, Xiang-You Huang

A. M. Perelomov, Y B Zeldovich

Discrete spectrum continuous spectrum analytic properties of the wave function the green's function and perturbation theory quasi-classical approximation exact solutions of certain non-stationary problems quasi-stationary states. Appendices: Schroedinger equation spectrum in specific cases quasi-classical properties of the highly excited levels in the Coulomb field.

Mohsen Razavy

The close connection between the Jacobi function for a velocity-dependent dissipative system and the nonlinear Schrödinger–Langevin equation is used to study some of the features of the latter equation. Starting with the Hamiltonian for a classical system, different forms of the Jacobi generating function are obtained. With the help of these, corresponding solutions of the nonlinear wave equation are studied. It is found that the solution of the wave equation is not unique, and that it admits quasi-stationary, decaying, and asymptotically stationary solutions. Since this nonlinear wave equation is derivable from a classical generating function, it preserves some of the characteristic properties of the linear quantum theory. Among these are: (a) the lack of any correlation between noninteracting particles moving in a viscous medium, (b) the gauge independence of the observable quantities, and (c) the constancy of the density of states in phase space. This discussion can also be extended to the problem of quantal description of a harmonically bound radiating electron.

A. I. Greiser

Antonio Rodríguez, Fernando Dantas Nobre, Constantino Tsallis

This paper studies the duration of quasi-stationary states, typical of long-range-interacting Hamiltonians where negative specific heat emerges. For the classical Heisenberg d-dimensional model, the authors show a universal behavior on the time evolution of the average kinetic energy per particle as a function of dimension, system size, and range of the interactions.