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The Schrodinger equation for stationary states in a central potential is studied in an arbitrary number of spatial dimensions, say q. After transformation into an equivalent equation, where the coefficient of the first derivative vanishes,…
We present the bound state solutions of the Schr\"odinger equation with generalized inverted hyperbolic potential using the Nikiforov-Uvarov method. We obtain the energy spectrum and the wave function with this potential for arbitrary -…
This work is devoted to non-linear stochastic Schr\"odinger equations with multiplicative fractional noise, where the stochastic integral is defined following the Riemann-Stieljes approach of Z\"ahle. Under the assumptions that the initial…
Recently, Olavo has proposed several derivations of the Schrodinger equation from different sets of hypothesis ("axiomatizations") [Phys. Rev. A 61, 052109 (2000)]. One of them is based on the infinitesimal inverse Weyl transform of a…
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…
It is shown that the Schrodinger equation for a large family of pairs of two-dimensional quantum potentials possess wavefuctions for which the amplitude and the phase are interchangeable, producing two different solutions which are dual to…
We have used Asymptotic Iteration Method (AIM) for obtaining the eigenvalues of the Schrodinger's equation for a deformed well problem representing trigonometric functions. By solving the problem, we have found that the Schrodinger's…
We obtain exact solutions of the 2D Schr\"odinger equation for Hydrogen atom with the lenear and Harmonic Potentials in noncommutative complex space, using the Power-series expansion method. Hence we can say that the Schr\"odinger equation…
This work develops a spherical-multipole expansion of Goldstein's acoustic analogy, for the prediction of tonal noise from rotating propellers. The acoustic field is expressed through spherical multipoles, which separate source integrals…
The approximate analytical bound state solution of the Schr\"odinger equation for the Manning-Rosen potential is carried out by taking a new approximation scheme to the orbital centrifugal term. The Nikiforov-Uvarov method is used in the…
Using Mathematica 3.0, the Schroedinger equation for bound states is solved. The method of solution is based on a numerical integration procedure together with convexity arguments and the nodal theorem for wave functions. The interaction…
Exact analytical expressions for the matrix elements of the Uehling potential in a basis of explicitly correlated exponential wave functions are presented. The obtained formulas are then used to compute with an improved accuracy the vacuum…
Discussed is the quantized version of the classical description of collective and internal affine modes as developed in Part I. We perform the Schr\"odinger quantization and reduce effectively the quantized problem from $n^{2}$ to $n$…
We introduce a renormalization procedure necessary for the complete description of the energy spectra of a one-dimensional stationary Schr\"odinger equation with a potential that exhibits inverse-square singularities. We apply and extend…
The simulation of strongly correlated many-electron systems is one of the most promising applications for near-term quantum devices. Here we use a class of eigenvalue solvers (presented in Phys. Rev. Lett. 126, 070504 (2021)) in which a…
Exact solution of Schrodinger equation for the Mie potential is obtained for an arbitrary angular momentum. The energy eigenvalues and the corresponding wavefunctions are calculated by the use of the Nikiforov-Uvarov method. Wavefunctions…
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)…
The non-relativistic three-body Schr\"odinger equation of the heteronuclear molecular ion HD$^+$ is solved in perimetric coordinates using the Lagrange-mesh method. Energies and wave functions of the four lowest vibrational bound or…
Atomic and molecular breakup reactions, such as multiple-ionisation, are described by a driven Schr\"odinger equation. This equation is equivalent to a high-dimensional Helmholtz equation and it has solutions that are outgoing waves,…
We present a bi-confluent Heun potential for the Schr\"odinger equation involving inverse fractional powers and a repulsive centrifugal-barrier term the strength of which is fixed to a constant. This is an infinite potential well defined on…