## Abstract

Eigenstates of the annihilation type operator U = C + iS, where C and S are the "cosine" and "sine" operators for harmonic oscillator phase, are shown to be closely related to thermal equilibrium states of the oscillator and to provide a new interpretation of the thermal equilibrium density operator. The problem of creating such states is considered and a general theorem is established leading to the construction of interaction Hamiltonians which transform the eigenstates of U among themselves and, in particular, create them from the oscillator ground state. These Hamiltonians lead to representations of the Lie algebras of O(2,1) and O(3). It is suggested that the mathematical technique used, in which generalized U-type operators provide the link between a group and its representations, has its own intrinsic interest for the study of Lie groups.

Original language | English |
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Pages (from-to) | 746-756 |

Number of pages | 11 |

Journal | Journal of Mathematical Physics |

Volume | 14 |

Issue number | 6 |

DOIs | |

State | Published - 1973 |