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Springer eBooks

Harmonic Oscillator States in Finite Dimensional Hilbert Space

Adam Miranowicz, Tomáš Opatrný, J. Bajer

Published Jan 1, 1997• 0 citations
Publisher
DOI
10.1007/978-94-015-8796-9_11

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It is shown that the state vector of a harmonic oscillator in a finite-dimensional Hilbert space changes sign only when the Hilbert space is of even dimension. The cyclic geometric phase for this finite-dimensional Hilbert-space harmonic oscillator is calculated. The effect of the finiteness of the Hilbert space on the dynamical and geometric phase change of a harmonic oscillator during a complete cycle is studied. In the limit of an infinite-dimensional case, the expressions reduce to the well known results.
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