Related papers: Dual wavefunctions in two-dimensional quantum mech…
An exactly solvable position-dependent mass Schr\"odinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing superintegrable two-dimensional systems…
The spectrum of r-1 and r-2 type potentials of diatomic molecules in radial Schrodinger equation are calculated by using the formalism of asymptotic iteration method. The alternative method is used to solve eigenvalues and eigenfunctions of…
Quantum scattering by a one-dimensional odd potential proportional to the square of the distance to the origin is considered. The Schr\"odinger equation is solved exactly and explicit algebraic expressions of the wavefunction are given. A…
Orthogonal Polynomials in Quantum Mechanics. Exact solutions of the Schrodinger equation with the hyperbolic Scarf potential (Scarf II) in terms of Romanovski polynomials. Among the applications included is the solution of the problem of an…
The Schr\"odinger-like equations for the marginal and conditional probability amplitudes resulting from the exact factorization of the wavefunction of a two-component system are derived in a form that is invariant to gauge and coordinate…
A simple and explicit technique for the numerical solution of the two-particle, time-dependent Schr\"{o}dinger equation is assembled and tested. The technique can handle interparticle potentials that are arbitrary functions of the…
This is the second article in a series where we succeed in enlarging the class of solvable problems in one and three dimensions. We do that by working in a complete square integrable basis that carries a tridiagonal matrix representation of…
Exactly solvable models play an extremely important role in many fields of quantum physics. In this study, the Schr\"{o}dinger equation is applied for a solution of a two--dimensional (2D) problem for two particles interacting via Kratzer,…
We show that the Schr\"odinger equation can be derived assuming the Galilean covariance of a generic wave equation and the validity of the de Broglie's wave-particle duality hypothesis. We also obtain from this set of assumptions the…
A nonlinear wave equation that describes different nonlinear effects in various fields of research was considered. In two particular cases, this equation was reduced to the Sine-Gordon equation and the Born-Infeld equation. Using the slowly…
For a given many-electron molecule, it is possible to define a corresponding one-electron Schr\"odinger equation, using potentials derived from simple atomic densities, whose solution predicts fairly accurate molecular orbitals for single-…
Two different approaches are formulated to analyze two-dimensional quantum models which are not amenable to standard separation of variables. Both methods are essentially based on supersymmetrical second order intertwining relations and…
Various dualities are summarized. Based on the universal wave-particle duality, along an opposite direction of the developed quantum mechanics, we use a method where the wave quantities frequency and wave length are replaced on various…
We obtain analytic solution of the time-independent Schrodinger equation in two dimensions for a charged particle moving in the field of an electric quadrupole. The solution is written as a series in terms of special functions that support…
By expressing the Schr\"odinger wave function in the form $\psi=Re^{iS/\hbar}$, where $R$ and $S$ are real functions, we have shown that the expectation value of $S$ is conserved. The amplitude of the wave ($R$) is found to satisfy the…
It is proved that when solving Schroedinger equations for radially symmetric potentials the effect of higher dimensions on the radial wave function is equivalent to the effect of higher angular momenta in lower dimensional cases. This…
We study the quantum dynamics of diatomic molecule driven by a circularly polarized resonant electric field. We look for a quantum effect due to classical chaos appearing due to the overlapping of nonlinear resonances associated to the…
It is proposed that the paradox of wave-particle duality in quantum mechanics may be resolved using a physical picture analogous to magnetic domains. Within this picture, a quantum particle represents a coherent region of a quantum wave…
We propose that the Schrodinger equation results from applying the classical wave equation to describe the physical system in which subatomic particles play random motion, thereby leading to quantum mechanics. The physical reality described…
The Schrodinger equation for the rotational-vibrational (ro-vibrational) motion of a diatomic molecule with empirical potential functions is solved approximately by means of the Nikiforov-Uvarov method. The approximate ro-vibratinal energy…