A relativistic quantum harmonic oscillator in 3+1 dimensions is derived from a quaternionic non-relativistic oscillator. This equation also yields the Klein-Gordon wave with covariant (space-time dependent) mass. mass quantized and given by $m_{*n}^2=m_\omega^2\left(n_r^2-1-\beta\,\left(n+1\right)\right)\,,$ where $m_\omega=\frac{\hbar\omega}{c^2}\,,$ $\beta=\frac{2mc^2}{\hbar\,\omega}\, $, $n$...

We study weak-coupling perturbation expansions for the ground-state energy of the Hamiltonian with the generalized spiked harmonic oscillator potential V (x) = Bx + A x + λ x , and also for the bottoms of the angular momentum subspaces labelled by l = 0, 1, . . . , in N -dimensions corresponding to the spiked harmonic oscillator potential V (x) = x + λ x , where α is a real positive parameter. ...

This paper represents a novel second harmonic power combining oscillator using mutually synchronized Gunn diodes embedded on slot line resonators. A both-sided MIC technology is adopted in the oscillator. The oscillator consists of Gunn diodes, slot line resonators and microstrip lines. By embedding Gunn diodes on slot line resonators, desired harmonic RF signal can be generated very easily. Th...

Objective...........................................................................................................................1 Harmonic Oscillators........................................................................................................1 Tuned Circuit' Oscillator...................................................................................................2 Experiment ...

— We prove stability of the bound states for the quantum harmonic oscillator under non-resonant, time quasi-periodic perturbations by proving that the associated Floquet Hamiltonian has pure point spectrum. Résumé (Stabilité de l’oscillateur harmonique quantique sous les perturbations quasipériodiques) Nous démontrons la stabilité des états bornés de l’oscillateur harmonique sous les perturbati...

‎We consider the oscillator group equipped with‎ ‎a biinvariant Lorentzian metric‎. ‎Some geometrical properties of this space and the harmonicity properties of left-invariant vector fields on this space are determined‎. ‎In some cases‎, ‎all these vector fields are critical points for the energy functional‎ ‎restricted to vector fields‎. ‎Left-invariant vector fields defining harmonic maps are...

The potential function of Lippincott and Schroeder for linear hydrogen bond has been re-examined and extended to nonlinear hydrogen bond. The parameters originally introduced to the potential function by Lippincott and Schroeder have been determined from the structural parameters such as 0.. .Odistance 0-H bond distance, H.. .O distance and HOO angle. Thevalidity of harmonic oscillator appr...

The quantum constraint equations for a relativistic three-dimensional harmonic oscillator are shown to find concise expression in terms of Lorentz covariant ladder operators. These ladder operators consist of two conjugate 4-vectors that are each constrained to generate three linearly independent combinations of ladder operator components for raising and lowering the eigenstates of the oscillat...