Accession Number N20120010663
Title Variance of the Quantum Dwell Time for a Nonrelativistic Particle.
Publication Date Jan 2012
Media Count 19p
Personal Author G. Hahne
Abstract Munoz, Seidel, and Muga (Phys. Rev. A 79, 012108 (2009)), following an earlier proposal by Pollak and Miller (Phys. Rev. Lett. 53, 115 (1984)) in the context of a theory of a collinear chemical reaction, showed that suitable moments of a two-flux correlation function could be manipulated to yield expressions for the mean quantum dwell time and mean square quantum dwell time for a structureless particle scattering from a time-independent potential energy field between two parallel lines in a two-dimensional spacetime. The present work proposes a generalization to a charged, nonrelativistic particle scattering from a transient, spatially confined electromagnetic vector potential in four-dimensional spacetime. The geometry of the spacetime domain is that of the slab between a pair of parallel planes, in particular those defined by constant values of the third (z) spatial coordinate. The mean Nth power, N = 1, 2, 3, . . ., of the quantum dwell time in the slab is given by an expression involving an N-flux-correlation function. All these means are shown to be nonnegative. The N = 1 formula reduces to an S-matrix result published previously (G. E. Hahne, J. Phys. A 36, 7149 (2003)); an explicit formula for N = 2, and of the variance of the dwell time in terms of the S-matrix, is worked out. A formula representing an incommensurability principle between variances of the output-minus-input flux of a pair of dynamical variables (such as the particle s time flux and others) is derived.
Keywords Correlation
Electromagnetism
Formalism
Nonrelativistic mechanics
Operators(Mathematics)
Particles
Quantum theory
S matrix theory
Schroedinger equation
Space-time functions
Variance(Statistics)


 
Source Agency National Aeronautics and Space Administration
NTIS Subject Category 51B - Aeronautics
Corporate Author National Aeronautics and Space Administration, Moffett Field, CA. Ames Research Center.
Document Type Journal article
Title Note N/A
NTIS Issue Number 1226
Contract Number N/A

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