In the Heisenberg picture, the generalized invariant and exact quantum motions are found for a time-dependent forced harmonic oscillator. We find the eigenstate and the coherent state of the invariant and show that the dispersions of these quantum states do not depend on the external force. Our formalism is applied to several interesting cases. ∗Electronic address: [email protected] †Electr...

The harmonic oscillator in anti de Sitter space(AdS) is discussed. We consider the harmonic oscillator potential and then time independent Schrodinger equation in AdS space. Then we apply the supersymmetric Quantum Mechanics approach to solve our differential equation. In this paper we have solved Schrodinger equation for harmonic oscillator in AdS spacetime by supersymmetry approach. The shape...

Systems of globally coupled phase oscillators can have robust attractors that are heteroclinic networks. We investigate such a heteroclinic network between partially synchronized states where the phases cluster into three groups. For the coupling considered there exist 30 different three-cluster states in the case of five oscillators. We study the structure of the heteroclinic network and demon...

1. AN EXPERIMENT WITH COUPLED OSCILLATORS. We begin with an experiment that requires minimal equipment: you just need your left and right forefingers. To get warmed up, first point your right forefinger in the natural way (we refer to this position as the “equilibrium position”). Next move your right forefinger back and forth in a motion that could be graphed as shown in Figure 1, where the dis...

We review the experimental constraints on additional macroscopic Yukawa forces for interaction ranges below 1 cm, and summarize several theoretical predictions of new forces in this region. An experiment using 1 kHz mechanical oscillators as test masses should be sensitive to much of the parameter space covered by the predictions.