We present some general results for the time-dependent mass Hamiltonian problem with H = − 2e∂xx + h(2)(t)e2ν(t)x2, where ν(t) is a continuous function of t. This Hamiltonian corresponds to a time-dependent mass (TM) Schrödinger equation with the restriction that there are only P 2 and X2 terms. We give the specific transformations to a different quadratic Schrödinger(TQ) equation and to a diff...

We present some general results for the time-dependent mass Hamiltonian problem with H = − 2e∂xx + h(2)(t)e2νx2. This Hamiltonian corresponds to a time-dependent mass (TM) Schrödinger equation with the restriction that there are only P 2 and X2 terms. We give the specific transformations to a different quantum Schrödinger(TQ) equation and to a different time-dependent oscillator (TO) equation. ...

In this paper, we attack the specific time-dependent Hamiltonian problem H = − 1 2 e Υ(t−to) ∂ xx + 1 2 ω 2 e −Υ(t−to) x 2. This corresponds to a time-dependent mass (T M) Schrödinger equation. We give the specific transformations to i) the more general quadratic (T Q) Schrödinger equation and to ii) a different time-dependent oscillator (T O) equation. For each Schrödinger system, we give the ...

We investigate the validity of Gaussian lower bounds for solutions to an electromagnetic Schrödinger equation with a bounded time-dependent complex electric potential and time-independent vector magnetic potential. prove that, if suitable geometric condition is satisfied by potential, then positive masses inside region at single time propagate outside region, provided average in space–time cyli...

We describe a parallel algorithm for solving the time-independent 3d Schrödinger equation using the finite difference time domain (FDTD) method. We introduce an optimized parallelization scheme that reduces communication overhead between computational nodes. We demonstrate that the compute time, t, scales inversely with the number of computational nodes as t ∝ (Nnodes). This makes it possible t...

Interaction and correlation effects in quantum dots play a fundamental role in defining both their equilibrium and transport properties. Numerical methods are commonly employed to study such systems. In this paper we investigate the numerical calculation of quantum transport of electrons in spherical centered defect InGaAs/AlGaAs quantum dot (SCDQD). The simulation is based on the imaginary time...

By applying the WKB (Wentzel, Kramers, Brillouin) approximation, we search for bound state solutions to time-independent Schrödinger equation an attractive inverse-square potential and anharmonic oscillators that stem from interaction of a point charge with radial electric fields. We focus on states associated s-waves. Further, obtain revival time each case studied.

It is shown that the eigenvalue problem for the Hamiltonians of the standard form, H = p/(2m) + V (x), is equivalent to the classical dynamical equation for certain harmonic oscillators with time-dependent frequency. This is another indication of the central role played by time-dependent harmonic oscillators in quantum mechanics. The utility of the known results for eigenvalue problem in the so...

In this paper an efficient and accurate method for simulating the propagation of a localized solution of the Schrödinger equation with a smooth potential near the semiclassical limit is presented. We are interested computing arbitrarily accurate solutions when the non dimensional Planck’s constant, e, is small, but not negligible. The method is based on a time dependent transformation of the in...

We summarize unusual bound or localized states in quantum mechanics. Our guide through these intriguing phenomena is the classical physics of the upside–down pendulum, taking advantage of the analogy between the corresponding Newton’s equation of motion and the time independent Schrödinger equation. We discuss the zero–energy ground state in a three–dimensional, spatially oscillating, potential...