Two-dimensional (2D) visible crystal-structure patterns analogous to the quantum harmonic oscillator (QHO) have been experimentally observed in the near- and far-fields of a self-frequency-doubling (SFD) microchip laser. Different with the fundamental modes, the localization of the SFD light is changed with the propagation. Calculation based on Hermite-Gaussian (HG) functions and second harmoni...

Most quantum tomographic methods can only be used for one-dimensional problems. We show how to infer the quantum state of a non-relativistic N-dimensional harmonic oscillator system by simple inverse Radon transforms. The procedure is equally applicable to finding the joint quantum state of several distinguishable particles in different harmonic oscillator potentials. A requirement of the proce...

We study the preparation of entangled pure Gaussian states via reservoir engineering. In particular, we consider a chain consisting of (2א+ 1) quantum harmonic oscillators where the central oscillator of the chain is coupled to a single reservoir. We then completely parametrize the class of (2א+1)-mode pure Gaussian states that can be prepared by this type of quantum harmonic oscillator chain. ...

This paper studies a suitably normalized set of generalized Hermite polynomials and sets down a relevant Mehler formula, Rodrigues formula, and generalized translation operator. Weighted generalized Hermite polynomials are the eigenfunctions of a generalized Fourier transform which satisfies an F. and M. Riesz theorem on the absolute continuity of analytic measures. The Bose-like oscillator cal...

A program able to use hybrid free rotor plus harmonic oscillator basis functions for the variational study of large and small amplitude vibrations is developed. The Hamiltonian matrix elements between harmonic oscillator eigenfunctions and polynomial terms are calculated using a recursive algorithm. This technique permits use of only one basic algorithm to compute the kinetic and potential part...

Operator angle-action variables are studied in the frame of the SU(2) algebra, and their eigenstates and coherent states are discussed. The quantum mechanical addition of actionangle variables is shown to lead to a novel non commutative Hopf algebra. The group contraction is used to make the connection with the harmonic oscillator. Presented at the ”Harmonic Oscillators” Workshop University of ...

Abstract We prove that smooth Wigner–Weyl spectral sums at an energy level E exhibit Airy scaling asymptotics across the classical surface Σ . This was proved earlier by authors for isotropic harmonic oscillator and proof is extended in this article to all quantum Hamiltonians − ℏ 2 Δ + V where a confining potential with most quadratic growth infinity. The main tools are Herman–Kluk initial val...

A formalism is developed to obtain the energy eigenvalues of spatially confined quantum mechanical systems in the framework of the usual Wentzel-Kramers-Brillouin (WKB) and Modified Airy Function (MAF) methods. To illustrate the working rule, the techniques are applied to 3 different cases, viz. the confined 1-dimensional harmonic and quartic oscillators, and a boxed-in charged particle subject...

The problem of considering a macroscopic oscillator in terms of Quantum Mechanics is usually avoided because one can obtain the right results without using any quantum mechanical hypothesys. When, however, one whishes to use it as a device to detect extremely small displacements due to very weak forces, as in the gravitational wave detectors, one has to be careful in considering it as a mere ma...