Weisskopf-Wigner Decay Theory for the Energy-Driven Stochastic Schrödinger Equation

Details Weisskopf-Wigner Decay Theory for the Energy-Driven Stochastic Schrödinger Equation Weisskopf-Wigner Decay Theory for the Energy-Driven Stochastic Schrödinger Equation

2002-08-19

arxiv.org/abs/quant-ph/0208123v4

Physics

Quantum Physics

29 pages in RevTeX, Added Note, references added

Scientific paper

We generalize the Weisskopf-Wigner theory for the line shape and transition rates of decaying states to the case of the energy-driven stochastic Schr\"odinger equation that has been used as a phenomenology for state vector reduction. Within the standard approximations used in the Weisskopf-Wigner analysis, and assuming that the perturbing potential inducing the decay has vanishing matrix elements within the degenerate manifold containing the decaying state, the stochastic Schr\"odinger equation linearizes. Solving the linearized equations, we find no change from the standard analysis in the line shape or the transition rate per unit time. The only effect of the stochastic terms is to alter the early time transient behavior of the decay, in a way that eliminates the quantum Zeno effect. We apply our results to estimate experimental bounds on the parameter governing the stochastic effects.

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