We analyze the distribution of eigenvalues quantum-mechanical rotating harmonic oscillator by means Frobenius method. A suitable ansatz leads to a three-term recurrence relation for expansion coefficients. Truncation series yields some particular and eigenfunctions in exact analytical form. The former can be organized such way that one obtains information about whole spectrum model.

Characterization and suppression of noise are essential for the control harmonic oscillators in quantum regime. We measure spectrum a oscillator from low frequency to near resonance by sensing its response amplitude modulated periodic drives with qubit. Using motion trapped ion, we experimentally demonstrate two different implementations combined sensitivity 500 Hz 600 kHz. apply our method int...

Attempts to unify Gravity Theory and Quantum Field (QFT) under Loop (LQG), are diverse; a dividing line between classical quantum is sought with Schrödinger cat-state experiments. A Primordial Theory-based alternative presented, gravity-based harmonic oscillator developed. With theory applied at micro-scales gravity meso- macro-scales, this scale-gap contributes the conceptual problems associat...

In this work a non-linear efficiency optimization method for its application to an Injection-Locked High Efficiency Voltage Controlled Oscillator is presented. The proposed approach is based on the control of the harmonic content of the oscillator autonomous signal, which is accomplished through the use of an Auxiliary Generator and several multi-harmonic loads based on Arbitrarily Width-Modula...

A molecular system adsorbed on a dielectric surface is modeled as a damped harmonic oscillator driven by a sinusoidal external force. The exact propagator and wavefunction through the Feynman path integral method are obtained. The second-quantization of this system is carried out. Expectation values of several physical quantities are evaluartd. The amplitude for transitions between harmonic osc...

It is proved that the matrix elements b F n;n+k between harmonic oscillator eigenvectors of any smooth observable in the quantized Lobachevskii plane converge to the Fourier coeecients F k of the corresponding classical observable F(A;) at the classical limit n ! 1; ~ ! 0; n~ ! A, k xed, where A, are the oscillator action-angle variables. The Wigner functions are then deened and, as a consequen...

in this article, the effect of the nonextensivity parameter on the energy fluctuations of nonextensive systems is studied in two different versions of the tsallis statistical mechanics. once a general expression has been reported for the energy fluctuations in the second version (tsallis work in 1988), the energy fluctuations of an ideal gas and a harmonic oscillator are studied in the second a...

We revisit the radial oscillator from standpoint of a free realization. By using oscillator, namely, creation/annihilation operators harmonic we construct an operator that maps eigenfunctions to those oscillator. As polynomial part this relation, obtain Hermite polynomials Laguerre polynomials.

Berry phase of simple harmonic oscillator is considered in a general representation. It is shown that, Berry phase which depends on the choice of representation can be defined under evolution of the half of period of the classical motions, as well as under evolution of the period. The Berry phases do not depend on the mass or angular frequency of the oscillator. The driven harmonic oscillator i...