Abstract
We consider various harmonic-oscillator states in a finite-dimensional Hilbert space. In greater detail we analyze finite-dimensional coherent states defined either by truncation of a number-state expansion of the standard coherent states or by the action of the generalized finite-dimensional displacement operator on vacuum. Within these two approaches other finite-dimensional states are analyzed, including displaced number states, and even and odd coherent states. We propose some new definitions of the states in a finitedimensional Hilbert space and construct explicitly all these states in Fock representation. The number-phase Wigner function is computed for several states. Analytical results and numerically computed graphs are presented.
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Miranowicz, A., Opatrný, T., Bajer, J. (1997). Harmonic Oscillator States in Finite Dimensional Hilbert Space. In: Hakioğlu, T., Shumovsky, A.S. (eds) Quantum Optics and the Spectroscopy of Solids. Fundamental Theories of Physics, vol 83. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8796-9_11
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DOI: https://doi.org/10.1007/978-94-015-8796-9_11
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