Related papers: Dual wavefunctions in two-dimensional quantum mech…
We construct a relationship between integral and differential representation of second-order Jordan chains. Conditions to obtain regular potentials through the confluent supersymmetry algorithm when working with the differential…
We investigate wavepacket solutions for time-dependent Schoedinger equation in the presence of an exponentially decaying potential. Assuming for travelling wave solutions the phase to be a linear combination of the space and time…
In this paper we apply the formalism of the analytical signal theory to the Schrodinger wavefunction. Making use exclusively of the wave-particle duality and the principle of relativistic covariance, we actually derive the form of the…
The two-dimensional hydrogen-like atom in a constant magnetic field is considered. It is found that this is actually two separate problems. One for which the magnetic field causes an effective attraction between the nucleus and the electron…
We propose an analytical approach for computing the eigenspectrum and corresponding eigenstates of a hyperbolic double well potential of arbitrary height or width, which goes beyond the usual techniques applied to quasi-exactly solvable…
In this paper, we show that the Kirchhoff equations are derived from the Schr\"odinger equation by assuming the wave function to be a polynomial like solution. These Kirchhoff equations describe the evolution of $n$ point vortices in…
A separable $x-y$ model is solved for a specialized vector potential (no magnetic and weak electric fields) penetrating slowly\textbf{,} adiabatically into and across a rectangular box to which an electron is confined. The time-dependent…
Following the familiar analogy between the optical paraxial wave equation and the Schr\"odinger equation, we derive the optimal, real-valued wave function for focusing in one and two space dimensions without the use of any phase component.…
The second-order differential equation for the Uehling potential is derived explicitly. The right side of this differential equation is a linear combination of the two Macdonald's functions $K_{0}(b r)$ and $K_{1}(b r)$. This central…
This paper presents analytical solutions for eigenvalues and eigenfunctions of the Schr\"odinger equation in higher dimensions, incorporating the Dunkl operator. Two fundamental quantum mechanical problems are examined in their exact forms:…
A system of two bilinearly coupled harmonic oscillators has been solved analytically by using the Born-Oppenheimer (BO) product wavefunction ansatz and the phase-space bound trajectory approach [J. S. Molano et al., Chem. Phys. Lett.…
We derive analytic expressions of the recursive solutions to the Schr\"{o}dinger's equation by means of a cutoff potential technique for one-dimensional piecewise constant potentials. These solutions provide a method for accurately…
Two essential shortcomings of the axiomatics of wave mechanics are revealed, which make its consistent interpretation impossible. The first is that the standard formulation of the superposition principle contradicts the exact solutions of…
Approximate bound state solutions of the Dirac equation with -deformed Woods-Saxon plus a new generalized ring-shaped potential are obtained for any arbitrary L-state. The energy eigenvalue equation and corresponding two-component wave…
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…
We present analytically the exact energy bound-states solutions of the Schrodinger equation in $D$-dimensions for a pseudoharmonic potential plus ring-shaped potential of the form $V(r,\theta)=D_{e}(\frac{r}{% r_{e}}-\frac{r_{e}}{r})…
In this study, we show that the energy eigenvalues and the eigenfunctions of the Schrodinger equation for the power-law and the logarithmic potential can be easily obtained by using variation technique for special type wave functions. The…
The two-dimensional hydrogen atom in an external magnetic field is considered in the context of phase space. Using solution of the Schr\"{o}dinger equation in phase space the Wigner function related to the Zeeman effect is calculated. For…
A two-time quantum theory of a system of two particles with the direct electromagnetic interaction based on a quantum version of the action principle is considered. An analog of Schrodinger equation for the system is obtained.
In this paper, a multi-dimensional fractional wave equation that describes propagation of the damped waves is introduced and analyzed. In contrast to the fractional diffusion-wave equation, the fractional wave equation contains fractional…