Probability operator of a harmonic oscillator

M. M. Ninan, Z. Stipčević

The transition probability of a linearly forced harmonic oscillator system is derived by expanding the evolution operator using an expansion theorem valid for operators obeying the commutation law, (A, B) = 1.

Sujit Basu and I A Lyabis

B. V. Rajarama Bhat, Kalyanapuram Rangachari Parthasarathy

Matyas I. Mechler, Margarita A. Man’ko, Vladimir I. Man’ko +1 more

We determine the evolving probability representation of entangled cat states in the potential of either the harmonic oscillator or the inverted oscillator, assuming that the states are initially prepared in the potential of the harmonic oscillator. Such states have several applications in quantum information processing. The inverted quantum harmonic oscillator, where the potential energy corresponds to imaginary frequencies of the oscillator, can be applied in relation to cosmological problems. We also determine the evolving probability representation of cat states of an oscillating spin-1/2 particle of the inverted oscillator, in which the time evolution of the spin state is described by an arbitrary unitary operator. The properties of the determined entangled probability distributions are discussed.

Francisco Marcelo Fernández

A simple and straightforward method is presented for calculating transition probabilities for the driven harmonic oscillator. The procedure does not require the explicit calculation of neither the time-evolution operator nor the Green’s function. As a result, a recurrence relation for the transition probabilities is obtained.

B. B. Varga, S. Ø. Aks