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 ...

Concepts of supersymmetry and parasupersymmetry known for the one-dimensional stationary Schrödinger equation are generalized to the time-dependent equation. Our approach is based on differential transformation operators for the non-stationary Schrödinger equation called Darboux transformation operators and on chains of such operators. As an illustration new exactly solvable time-dependent pote...

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...

The second order (in time) Schrödinger equation is proposed. The additional term (in comparison to Schrödinger equation) describes the interaction of particles with vacuum filled with virtual particle – antiparticle pairs (zitterbewegung).

of the periodic nonlinear Schrödinger equation, where u(x, t) is a complex valued function in the class of smooth period one functions. In this work, we explain in what sense the generic level set of the constants of motion for the periodic nonlinear Schrödinger equation is an infinite dimensional torus, why the solution of the Hamiltonian equation is almost periodic in time, and describe how n...

Abstract. We exhibit a change of variables that turns the critical nonlinear Schrödinger equation into the critical nonlinear Schrödinger equation with isotropic harmonic potential, in any space dimension. This change of variables is isometric on L, and bijective on some time intervals. Using the known results for the critical nonlinear Schrödinger equation, this provides information for the pr...

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 timedependent 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. Fo...