Quantum Mechanical Reflection Resonances

2006/10/27 by Caden, Erica, Gilmore, Robert
#FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.quant-ph/0610239

Abstract

Resonances in the reflection probability amplitude r(E) can occur in energy ranges in which the reflection probability R(E)=|r(E)|² is 1. They occur as the phase phi(E) defined by r(E) = t*(E)/t(E) = 1e^{i 2phi(E)} undergoes a rapid change of pi radians. During this transition the phase angle exhibits a Lorentzian profile in that d(phi(E))/dE ~= 1/[(E-E₀)²+(hbar*gamma/2)²]. The energy E₀ identifies the location of a quasi-bound state, gamma measures the lifetime of this state, and t(E) is a matrix element of the transfer operator. Methods for computing and measuring these resonances are proposed.

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