Related papers: A new approach to solving the Schr\"odinger equati…
In this paper, we reformulate the semi-classical Schr\"odinger equation in the presence of electromagnetic field by the Gaussian wave packets transform. With this approach, the highly oscillatory Schr\"odinger equation is equivalently…
The Schrodinger equation has been considered to be a postulate of quantum physics, but it is also perceived and derived heuristically as the quantum equivalent of the classical energy relation. We indicate that the Schrodinger equation…
Here we present a transformation that maps the Schrodinger equation of quantum mechanics to the incompressible Euler equations of fluid mechanics. The transformation provides a wave solution and a potential function based on fluid…
For the first time, a nonlinear Schr\"odinger equation of the general form is considered, depending on time and two spatial variables, the potential and dispersion of which are specified by two arbitrary functions. This equation naturally…
We discuss the explicit construction of the Schroedinger equations admitting a representation through some family of general polynomials. Almost all solvable quantum potentials are shown to be generated by this approach. Some generalization…
We construct a variety of new exactly-solvable quantum systems, the potentials of which are given in terms of Lambert-W functions. In particular, we generate Schr\"odinger models with energy-dependent potentials, conventional Schr\"odinger…
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…
The Schr\"{o}dinger equation is solved for the case of a particle confined to a small region of a box with infinite walls. If walls of the well are moved, then, due to an effective quantum nonlocal interaction with the boundary, even though…
The Schr\"odinger equation with a Lennard-Jones potential is solved by using a procedure that treats in a rigorous way the irregular singularities at the origin and at infinity. Global solutions are obtained thanks to the computation of the…
A solution of the scattering problem is obtained for the Schr\"odinger equation with the potential of induced dipole interaction, which decreases as the inverse square of the distance. Such a potential arises in the collision of an incident…
A nonlinear generalisation of Schrodinger's equation had previously been obtained using information-theoretic arguments. The nonlinearities in that equation were of a nonpolynomial form, equivalent to the occurence of higher-derivative…
We transform the Schr\"odinger wave equation to a nine-parameter Heun-type differential equation. Using our solutions of the latter in [J. Math. Phys. 59 (2018) 113507], we are able to identify the associated potential function, energy…
We introduce a new exactly integrable potential for the Schr\"odinger equation for which the solution of the problem may be expressed in terms of the Gauss hypergeometric functions. This is a potential step with variable height and…
Bohmian mechanics is a deterministic theory of quantum mechanics that is based on a set of n velocity functions for n particles, where these functions depend on the wavefunction from the n-body time-dependent Schroedinger equation. It is…
The Schr\"{o}dinger equation is solved exactly for some well known potentials. Solutions are obtained reducing the Schr\"{o}dinger equation into a second order differential equation by using an appropriate coordinate transformation. The…
We study the possible vanishing order of solutions to Schrodinger equation in case the potential is a bounded function. We give an upper bound on compact manifold. We also show that this result is sharp.
The wavefunction for the multiparticle Schr\"odinger equation is a function of many variables and satisfies an antisymmetry condition, so it is natural to approximate it as a sum of Slater determinants. Many current methods do so, but they…
Quantum theory has been remarkably successful in providing an understanding of physical systems at foundational scales. Solving the Schr\"odinger equation provides full knowledge of all dynamical quantities of the physical system. However…
Schrodinger path to the quantum mechanical wave equation was heuristic and guided more by physical intuition than formal deduction. Here we derive the Schrodinger equation for the particle wave function, assuming that it has a meaning of…
Wave/Schr\"{o}dinger equations with potentials naturally originates from both the quantum physics and the study of nonlinear equations. The distractive Coulomb potential is a quantum mechanical description of distractive Coulomb force…