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Newton-Equivalent Hamiltonians for the Harmonic Oscillator

✍ Scribed by A. Degasperis; S.N.M. Ruijsenaars

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
93 KB
Volume
293
Category
Article
ISSN
0003-4916

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✦ Synopsis

We consider a one-parameter family of Hamilton functions yielding the Newton equation of the harmonic oscillator, ẍ + Ο‰ 2 x = 0. The parameter may be viewed as the speed of light c, the nonrelativistic limit c β†’ ∞ yielding the usual Hamiltonian. For c < ∞, the classical Hamiltonians are the product of a function of x and a function of p. In the quantum case, with a suitable ordering, we explicitly find the spectrum and the eigenfunctions of the Hamiltonian.

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