相关论文: Equivalence of two alternative approaches to Schro…

For the first time, the general nonlinear Schr\"odinger equation is investigated, in which the chromatic dispersion and potential are specified by two arbitrary functions. The equation in question is a natural generalization of a wide class…

This paper presents the exact ground state solution for a diatomic particle system with position-dependent complex mass under action of a complex Morse potential in the quantum domain. By solving the position-dependent Schr\"odinger…

We obtain exact solutions of the one-dimensional Schrodinger equation for some families of associated Lame potentials with arbitrary energy through a suitable ansatz, which may be appropriately extended for other such a families. The…

We introduce a numerical method, based on finite elements and lattice gauge theory, to compute approximate solutions to Schr\"odinger and Pauli equations. The crucial geometric property of the method is discrete gauge invariance. The main…

We discuss a new approach to solve the low lying states of the Schroedinger equation. For a fairly large class of problems, this new approach leads to convergent iterative solutions, in contrast to perturbative series expansions. These…

The Schrodinger equations which are exactly solvable in terms of associated special functions are directly related to some self-adjoint operators defined in the theory of hypergeometric type equations. The fundamental formulae occurring in…

We prove that if a solution of the discrete time-dependent Schr\"odinger equation with bounded real potential decays fast at two distinct times then the solution is trivial. For the free Shr\"odinger operator and for operators with…

An approximate method is proposed to solve position dependent mass Schr\"odinger equation. The procedure suggested here leads to the solution of the PDM Schr\"odinger equation without transforming the potential function to the mass space or…

We analyse the exact solutions of a conditionally-solvable Schr\"odinger equation with a rational potential. From the nodes of the exact eigenfunctions we derive a connection between the otherwise isolated exact eigenvalues and the actual…

With the consideration of spherical symmetry for the potential and mass function, one-dimensional solutions of non-relativistic Schrodinger equations with spatially varying effective mass are successfully extended to arbitrary dimensions…

The outlook of a simple method to generate localized (soliton-like) potentials of time-dependent Schrodinger type equations is given. The conditions are discussed for the potentials to be real and nonsingular. For the derivative Schrodinger…

The second order $N$-dimensional Schr\"odinger equation with pseudoharmonic potential is reduced to a first order differential equation by using the Laplace transform approach and exact bound state solutions are obtained using convolution…

The asymptotic iteration method is used to find exact and approximate solutions of Schroedinger's equation for a number of one-dimensional trigonometric potentials (sine-squared, double-cosine, tangent-squared, and complex cotangent).…

The aim of this paper is to find the exact solutions of the Schrodinger equation. As is known, the Schrodinger equation can be reduced to the continuum equation. In this paper, using the non-linear Legendre transform the equation of…

We consider parabolic Schr\"odinger type equations associated to fractional powers of uniformly elliptic 2m-order operators with constant coefficients. Potentials and initial data are considered in suitable Morrey spaces. By means of…

The Schrodinger equation for stationary states is studied in a central potential V(r) proportional to the inverse power of r of degree beta in an arbitrary number of spatial dimensions. The presence of a single term in the potential makes…

We deal with the exact solutions of Schrodinger equation characterized by position-dependent effective mass via point canonical transformations. The Morse, Poschl-Teller and Hulthen type potentials are considered respectively. With the…

Exact solutions of the Schrodinger equation are obtained for the Rosen-Morse and Scarf potentials with the position-dependent effective mass by appliying a general point canonical transformation. The general form of the point canonical…

A construction method of infinite families of quasi-exactly solvable position-dependent mass Schr\"odinger equations with known ground and first excited states is proposed in a deformed supersymmetric background. Such families correspond to…

This report discusses two new ideas for using perturbation methods to solve the time-independent Schr\"odinger equation. The first concept begins with rewriting the perturbation equations in a form that is closely related to matrix…