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...