Cutoff Schrödinger equations in functional derivatives are solved via quantized Galerkin limit of antinormal functional Feynman integrals for Schrödinger equations in partial derivatives. Mathematics Subject Classification 2000: 81T08, 81T16; 26E15, 81Q05, 81S40.

Lie symmetries of the Schroedinger-Pauli equations for charged particles and quasirelativistic Schroedinger are classified. In particular a new superintegrable system with spin-orbit coupling is discovered.

Schrödinger equations in functional derivatives are solved via quantized Galerkin limit of antinormal functional Feynman integrals for Schrödinger equations in partial derivatives. Mathematics Subject Classification 2000: 81T08, 81T16; 26E15, 81Q05, 81S40.

We give an error analysis of Strang-type splitting integrators for nonlinear Schrödinger equations. For Schrödinger-Poisson equations with an H4-regular solution, a first-order error bound in the H1 norm is shown and used to derive a second-order error bound in the L2 norm. For the cubic Schrödinger equation with an H4-regular solution, first-order convergence in the H2 norm is used to obtain s...

Abstract. We study the dynamics of the Schrödinger equation with a fractional Laplacian (−∆), and the decoherence of the solution is observed in certain cases. Analytically, we find equations describing the dynamics of the expected position and expected momentum in the fractional Schödinger equation, equations that are the fractional counterpart of the Newtonian equations of motion for the non-...

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. ...

Time-dependent Schrödinger equation represents the basis of any quantum-theoretical approach. The question concerning its proper content in comparison to the classical physics has not been, however, fully answered until now. It will be shown that there is one-to-one physical correspondence between basic solutions (represented always by one Hamiltonian eigenfunction only) and classical ones, as ...

By using the Lie’s invariance infinitesimal criterion we obtain the continuous equivalence transformations of a class of nonlinear Schrödinger equations with variable coefficients. Starting from the equivalence generators we construct the differential invariants of order one. We apply these latter ones to find the most general subclass of variable coefficient nonlinear Schrödinger equations whi...