We show that for a one-dimensional Schrödinger operator with a potential, whose (j + 1)-th moment is integrable, the j-th derivative of the scattering matrix is in the Wiener algebra of functions with integrable Fourier transforms. We use this result to improve the known dispersive estimates with integrable time decay for the one-dimensional Schrödinger equation in the resonant case.

We extend the well-known trace formula for Hill’s equation to general one-dimensional Schrödinger operators. The new function ξ, which we introduce, is used to study absolutely continuous spectrum and inverse problems. In this note we will consider one-dimensional Schrödinger operators

We consider the real stationary two-dimensional Schrödinger equation. With the aid of any its particular solution we construct a Vekua equation possessing the following special property. The real parts of its solutions are solutions of the original Schrödinger equation and the imaginary parts are solutions of an associated Schrödinger equation with a potential having the form of a potential obt...

We present accurate numerical results for the one-dimensional stationary Schrödinger equation in case of three quantum problems: harmonic oscillator, radial a Hydrogen atom, and particle penetration through potential barrier. All them were solved by Numerov method with high accuracy we plot their wave functions using calculations. Furthermore, offer methods solving boundary value problems, eige...

The Schrödinger equation with the central potential is first studied in the arbitrary dimensional spaces and obtained an analogy of the two-dimensional Schrödinger equation for the radial wave function through a simple transformation. As an example, applying an ansatz to the eigenfunctions, we then arrive at an exact closed form solution to the modified two-dimensional Schrödinger equation with...

In a stationary case and for any potential, we solve the three-dimensional quantum Hamilton-Jacobi equation in terms of the solutions of the corresponding Schrödinger equation. Then, in the case of separated variables, by requiring that the conjugate momentum be invariant under any linear transformation of the solutions of the Schrödinger equation used in the reduced action, we clearly identify...

In this letter, we consider the Schrödinger equation for a well potential with varying width. We solve one dimensional Schrödinger equation subject to time-dependent boundary conditions for a spinless particle inside infinite potential well, both wall of which move opposite direction with different velocities υ1 and υ2, respectively. PACS numbers: 03.65.Ge Typeset using REVTEX

We develop a fourth order numerical method for the computation of multivalued physical observables (density, momentum, etc.) in the semiclassical limit of the one dimensional linear Schrödinger equation in the case of discontinuous potentials. We adopt the level set framework developed in [21] which allows one to compute the multivalued physical observables via solving the classical Liouville e...

We present an extension of the Gilbert-Pearson theory of subordinacy, which relates dimensional Hausdorff spectral properties of one-dimensional Schrödinger operators to the behavior of solutions of the corresponding Schrödinger equation. We use this theory to analyze these properties for several examples having the singular-continuous spectrum, including sparse barrier potentials, the almost M...