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Semiclassical and quantum analysis of a free-particle Hermite wave function

Strange, Paul (2014) Semiclassical and quantum analysis of a free-particle Hermite wave function. Physical Review A: Atomic, Molecular and Optical Physics, 89 (04). 044101. ISSN 1050-2947. (doi:10.1103/PhysRevA.89.044101)


In this Brief Report we discuss a solution of the free-particle Schrödinger equation in which the time and space dependence are not separable. The wave function is written as a product of exponential terms, Hermite polynomials, and a phase. The peaks in the wave function decelerate and then accelerate around t=0. We analyze this behavior within both a quantum and a semiclassical regime. We show that the acceleration does not represent true acceleration of the particle but can be related to the envelope function of the allowed classical paths. Comparison with other “accelerating” wave functions is also made. The analysis provides considerable insight into the meaning of the quantum wave function.

Item Type: Article
DOI/Identification number: 10.1103/PhysRevA.89.044101
Uncontrolled keywords: Physics of Quantum Materials
Subjects: Q Science > QC Physics > QC174.12 Quantum theory
Q Science > QC Physics > QC20 Mathematical Physics
Divisions: Faculties > Sciences > School of Physical Sciences > Functional Materials Group
Depositing User: Paul Strange
Date Deposited: 01 Apr 2014 15:05 UTC
Last Modified: 25 Jan 2020 04:05 UTC
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