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Lower and upper bounds for time-smoothed total transition probabilities and their rates

S Golden

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A formalism of time-smoothed total transition probabilities and their rates is developed which employs Laplace averages of these quantities. Under conditions pertinent to scattering processes, the Laplace-average formalism is shown to yield results equivalent to those obtained from a stationary-state formalism. Rigorous lower and upper bounds are obtained for the Laplace-averaged quantities which reduce to equalities for two-level systems. The lower bounds appear to be potentially useful estimating lower bounds for total cross sections of various processes.


PACS

03.65.Ca Formalism

03.65.Ge Solutions of wave equations: bound states

03.65.Fd Algebraic methods

MSC

81R15 Operator algebra methods (See also 46Lxx, 81T05)

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other quantum-mechanical equations

Subjects

Quantum information and quantum mechanics

Dates

Issue 6 (June 1976)



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