Abstract
This paper examines single-mode and two-mode Gaussian pure states (GPS), quantum mechanical pure states with Gaussian wave functions. These states are produced when harmonic oscillators in their ground states are exposed to potentials, or interaction Hamiltonians, that are linear or quadratic in the position and momentum variables (i.e., annihilation and creation operators) of the oscillators. The physical and group theoretical properties of these Hamiltonians and the unitary operators they generate are discussed. These properties lead to a natural classification scheme for GPS. Important properties of single-mode and two-mode GPS are discussed. An efficient vector notation is introduced, and used to derive many of the important properties of GPS and of the Hamiltonians and unitary operators associated with them.
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