PERTURBATIVE ANALYSIS OF UNCERTAINTY IN COHERENT STATES OF NEWTON-EQUIVALENT QUANTUM HARMONIC OSCILLATOR
Keywords:
Newton-equivalent quantum harmonic oscillator, coherent state, perturbation, uncertainty relationAbstract
Coherent states are quantum states which are importance for both theoretical and experimental sides. Their theoretical constructions in quantum harmonic oscillator are simple, but they possess many important properties. In this work, we study coherent states for Newton-equivalent quantum harmonic oscillator, which are models of a one-parameter family of Hamiltonians alternative to the standard quantum harmonic oscillator. When the value of the parameter tends to zero, one recovers the standard quantum harmonic oscillator. The coherent states are perturbatively constructed up to the second order in the parameter. Then the uncertainty relations for some of the states are considered. In particular, we consider the case || < 2, where is the complex number characterising the coherent states. The results suggest that the product of the uncertainty in measuring the position and the momentum takes, to a good approximation, the minimal value. This behaviour agrees with that of the coherent states for the standard quantum harmonic oscillator.
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