Related papers: A new approach to solving the Schr\"odinger equati…
A fundamental belief is that the formulism of relativistic quantum mechanics equations (RQMEs) should remain in low momentum motion. However, it is found that some formulas from RQMEs were lost in Schr\"odinger equation. For example, a free…
Quantum mechanics has about a dozen exactly solvable potentials. Normally, the time-independent Schroedinger equation for them is solved by using a generalized series solution for the bound states (using the Froebenius method) and then an…
The wavefunction of a particle is obtained from its intermediate states and interaction processes considered as happening concurrently. When the interaction is described by a potential, the energy of the particle is equal to its total…
We present a new hydrodynamic analogy of nonrelativistic quantum particles in potential wells. Similarities between a real variant of the Schr\"odinger equation and gravity-capillary shallow water waves are reported and analyzed. We show…
We analyze Bohm's potential effects both in the realms of Quantum Mechanics and Optics, as well as in the study of other physical phenomena described in terms of classical and quantum wave equations. We approach this subject by using…
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-…
The direct solution of the many-particle Schr\"odinger equation is computationally inaccessible for more than very few electrons. In order to surpass this limitation, one of the authors [X. Oriols, Phys. Rev. Lett. 2007, 98 (066803)] has…
We present the exact solution of the stationary Schr\"odinger equation equation for the potential $V=V_0/{\sqrt{x}}$. Each of the two fundamental solutions that compose the general solution of the problem is given by a combination with…
It is well known that Schr\"{o}dinger's equation is only suitable for the particle in conservative force field. In atomic and molecular field, a particle can suffer the action of non-conservative force. In this paper, a new quantum wave…
The molecular Schr\"odinger equation is rewritten in terms of non-unitary equations of motion for the nuclei (or electrons) that depend parametrically on the configuration of an ensemble of generally defined electronic (or nuclear)…
We study the behavior of solitary-wave solutions of some generalized nonlinear Schr\"odinger equations with an external potential. The equations have the feature that in the absence of the external potential, they have solutions describing…
From the point of view of Schr\"odingerism, a wavefunction-only philosophy, thermodynamics must be recast in terms of an ensemble of wavefunctions, rather than classical particle configurations or "found" values of Copenaghen Quantum…
We consider the problem of numerically solving the Schr\"odinger equation with a potential that is quasi periodic in space and time. We introduce a numerical scheme based on a newly developed multi-time scale and averaging technique. We…
We study the quantum behaviour of a particle moving in a one-dimensional double well potential. This double well is obtained by gluing together, at the origin, two shifted harmonic oscillator potentials. The Schr\"odinger equation is…
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…
In this paper we consider the one dimensional quantum hydrodynamics (QHD) system, with a genuine hydrodynamic approach. The global existence of weak solutions with large data has been obtained in [2, 3], in several space dimensions, by…
The wave functions of Boson and Fermion gases are known even when the particles have harmonic interactions. Here we generalise these results by solving exactly the N-body Schrodinger equation for potentials V that can be any function of the…
We present a conditionally exactly solvable singular potential for the one-dimensional Schr\"odinger equation which involves the exactly solvable inverse square root potential. Each of the two fundamental solutions that compose the general…
In this paper, we present a simple analytical method for obtaining a nonspreading solution of the time-dependent Schr\"odinger equation, which is given by the Airy function. The solution is derived by imposing a restriction on the phase…
An infinite family of closed-form solutions is exhibited for the Schroedinger equation for the potential $V(r) = -Z/\sqrt{|r|^{2} + a^{2}}$. Evidence is presented for an approximate dynamical symmetry for large values of the angular…