Method of generating functions for a quantum oscillator

V. S. Popov, M. A. Trusov

Mehdi Hage-Hassan

We determine the generating function of the harmonic oscillator by a new method. Using this generating function we derive the eigenfunctions of the moment p. We find that the normalization of these eigenfunctions is a real and not complex number with phase factor chosen equal one (standard books of quantum mechanics). We prove that the integral of the delta function is equal to one and we derive the oscillator propagator.

Govind S. Khandelwal

Edward B. Rockower, N. B. Abraham

A method is found for calculating the number generating function of a harmonic oscillator density matrix directly from the quantum characteristic function. This technique is used to interpret thermal noise in a model for an optical detector. The results clearly reveal an earlier misinterpretation and emphasise that the terminal noise is a statistically independent amplitude in the detector/harmonic oscillator which is superposed with an amplitude having the same statistical nature as the incident optical field.

Balraj Menon

Javier Alvarez-Jimenez, J. David Vergara

We introduce a new method to compute the Quantum Geometric Tensor, this procedure allows us to compute the Quantum Information Metric and the Berry curvature perturbatively for a theory with an arbitrary interaction Hamiltonian. The calculation uses the generating function method, and it is illustrated with the harmonic oscillator with a linear and a quartic perturbation.