نتایج جستجو برای: time independent schrödinger equation
تعداد نتایج: 2428460 فیلتر نتایج به سال:
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...
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...
In this paper an efficient and accurate method for simulating the propagation of a localized solution of the Schrödinger equation near the semiclassical limit is presented. We are interested computing arbitrarily accurate solutions when the non dimensional Plank’s constant, ε, is small, but not negligible. The method is based on a time dependent transformation of the independent variables, clos...
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...
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...
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).
This article considers the linear 1-d Schrödinger equation in (0, π) perturbed by a vanishing viscosity term depending on a small parameter ε > 0. We study the boundary controllability properties of this perturbed equation and the behavior of its boundary controls vε as ε goes to zero. It is shown that, for any time T sufficiently large but independent of ε and for each initial datum in H−1(0, ...
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...
We consider the semiclassical limit for the nonlinear Schrödinger equation. We introduce a phase/amplitude representation given by a system similar to the hydrodynamical formulation, whose novelty consists of including some asymptotically vanishing viscosity. We prove that the system is always locally well-posed in a class of Sobolev spaces, and globally well-posed for a fixed positive Planck c...
We demonstrate that complex point transformations can be used to construct non-Hermitian first integrals, time-dependent Dyson maps and metric operators for quantum systems. Initially we identify a transformation as map from an exactly solvable time-independent system explicitly Hamiltonian system. Subsequently employ the invariant latter Exploiting fact this is pseudo-Hermitian, corresponding ...
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