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...

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.

A variationally improved Sturmian approximation for solving time-independent Schrödinger equation is developed. This approximation is used to obtain the energy levels of a quartic anharmonic oscillator, a quartic potential, and a Gaussian potential. The results are compared with those of the perturbation theory, the WKB approximation, and the accurate numerical values.

The many-body wave function of a system of interacting particles confined by a time-dependent harmonic potential and perturbed by a time-dependent spatially homogeneous electric field is derived via the Feynman path-integral method. The wave function is comprised of a phase factor times the solution to the unperturbed time-dependent Schrödinger equation with the latter being translated by a tim...

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...

It is shown how to compute the instability rates for double-periodic solutions cubic NLS (nonlinear Schrödinger) equation by using Lax linear equations. The wave function modulus of periodic both in space and time coordinates; such generalize standing waves which have time-independent space-periodic modulus. Similar other equation, are spectrally unstable this related bands spectrum outside ima...

One-dimensional nonrelativistic systems are studied when time-independent potential interactions are involved. Their supersymmetries are determined and their closed subsets generating kinematical invariance Lie superalgebras are pointed out. The study of even supersymmetries is particularly enlightened through the already known symmetries of the corresponding Schrödinger equation. Three tables ...

The Gamow vector description of resonances is compared with the S-matrix and the Green function descriptions using the example of the square barrier potential. By imposing different boundary conditions on the time independent Schrödinger equation, we obtain either eigenvectors corresponding to real eigenvalues and the physical spectrum or eigenvectors corresponding to complex eigenvalues (Gamow...

In this paper, we probe the validity of the tunneling interpretation that is usually called forth in the literature to explain the phenomenon of particle production by time-independent classical electromagnetic backgrounds. We show that the imaginary part of the effective Lagrangian is zero for a complex scalar field quantized in a time-independent, but otherwise arbitrary, magnetic field. This...