7 research outputs found
A report on the nonlinear squeezed states and their non-classical properties of a generalized isotonic oscillator
We construct nonlinear squeezed states of a generalized isotonic oscillator
potential. We demonstrate the non-existence of dual counterpart of nonlinear
squeezed states in this system. We investigate statistical properties exhibited
by the squeezed states, in particular Mandel's parameter, second-order
correlation function, photon number distributions and parameter in
detail. We also examine the quadrature and amplitude-squared squeezing effects.
Finally, we derive expression for the -parameterized quasi-probability
distribution function of these states. All these information about the system
are new to the literature.Comment: Accepted for publication in J. Phys. A: Math. Theo
Exact quantization of a PT-symmetric (reversible) Li\'enard-type nonlinear oscillator
We carry out an exact quantization of a PT symmetric (reversible) Li\'{e}nard
type one dimensional nonlinear oscillator both semiclassically and quantum
mechanically. The associated time independent classical Hamiltonian is of
non-standard type and is invariant under a combined coordinate reflection and
time reversal transformation. We use von Roos symmetric ordering procedure to
write down the appropriate quantum Hamiltonian. While the quantum problem
cannot be tackled in coordinate space, we show how the problem can be
successfully solved in momentum space by solving the underlying Schr\"{o}dinger
equation therein. We obtain explicitly the eigenvalues and eigenfunctions (in
momentum space) and deduce the remarkable result that the spectrum agrees
exactly with that of the linear harmonic oscillator, which is also confirmed by
a semiclassical modified Bohr-Sommerfeld quantization rule, while the
eigenfunctions are completely different.Comment: 10 pages, 1 figure, Fast Track Communicatio
Coherent and Squeezed States: Introductory Review of Basic Notions, Properties, and Generalizations
A short review of the main properties of coherent and squeezed states is
given in introductory form. The efforts are addressed to clarify concepts and
notions, including some passages of the history of science, with the aim of
facilitating the subject for nonspecialists. In this sense, the present work is
intended to be complementary to other papers of the same nature and subject in
current circulation.Comment: 50 pages, misprints corrected, some new references included. To
appear in "Integrability, Supersymmetry and Coherent States. A Volume in
Honor of Professor Veronique Hussin