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One-Parameter Squeezed Gaussian States of Time-Dependent Harmonic Oscillator and Selection Rule for Vacuum States
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One-Parameter Squeezed Gaussian States of Time-Dependent Harmonic Oscillator and Selection Rule for Vacuum States
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By using the invariant method we find one-parameter squeezed Gaussian states for both time-independent and time-dependent oscillators. The squeezing parameter is expressed in terms of energy expectation value for time-independent case and represents the degree of mixing positive and negative frequency solutions for time-dependent case. A {\it minimum uncertainty proposal} is advanced to select uniquely vacuum states at each moment of time. We show that the Gaussian states with minimum uncertainty coincide with the true vacuum state for time-independent oscillator and the Bunch-Davies vacuum for a massive scalar field in a de Sitter spacetime.
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