On the symmetries and invariants of the harmonic oscillator

Gordon, T. J. (1986) On the symmetries and invariants of the harmonic oscillator. Journal of Physics A: Mathematical and General, 19 (2). pp. 183-189. ISSN 0305-4470

Full content URL: http://dx.doi.org/10.1088/0305-4470/19/2/014

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Item Type:Article
Item Status:Live Archive

Abstract

A general formulation of Noether's theorem is applied to the equation of a harmonic oscillator. The definition of symmetry includes the usual Lie invariance as a special case and (unlike standard formulations) generates the full set of invariants (i.e. gives closure under functional composition). The analysis for a time-dependent oscillator casts doubt on the importance of a known class of invariants. The existence of a Lagrangian function is shown to be inessential to the analysis.

Keywords:Quantum information, Quantum mechanics
Subjects:F Physical Sciences > F342 Quantum Mechanics
H Engineering > H100 General Engineering
Divisions:College of Science > School of Engineering
ID Code:11705
Deposited On:23 Aug 2013 09:09

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