Coherence: The Schrödinger equation

Bruce W. Shore, Michael Austin Johnson

We demonstrate the manner in which solutions of the (coherent) Schrödinger equation for multistep excitation approach those of an (incoherent) rate equation. For a two-level system, coherence produces oscillations about the mean rate-equation values. In more general N-level sequences the two types of solutions agree in the limit described by Ackerhalt and Eberly. We point out instances in which a simple rate equation cannot duplicate results of the Schrödinger equation.

David B. Cook

Alexandru Popa

In recent papers we presented a wave model for closed conservative bounded systems, whose behavior is described by the Schrodinger equation. For such a system, the Schrodinger equation is equivalent to the wave equation. The analysis of the wave properties reveals an intrinsic coherence of the electron motions. We approximate the fundamental and metastable states of laser active medium by closed conservative bounded systems. We show that the coherence of the laser radiation could be explained by a transition between these coherent states.

Philip Brenner, Vidar Thomée, Lars B. Wahlbin

V. Chithiika Ruby, Murugaian Senthilvelan

In this paper, we propose an algorithm to construct coherent states for an exactly solvable position dependent mass Schrödinger equation. We use point canonical transformation method and obtain ground state eigenfunction of the position dependent mass Schrödinger equation. We fix the ladder operators in the deformed form and obtain explicit expression of the deformed superpotential in terms of mass distribution and its derivative. We also prove that these deformed operators lead to minimum uncertainty relations. Further, we illustrate our algorithm with two examples, in which the coherent states given for the second example are new.