Related papers: Closed-form Second Solutions to the Coulombic Schr…
Solutions of the Schr\"odinger equation by spanning the wave function is a complete basis is a common practice is many-body interacting systems. We shall study the case of a two-dimensional quantum system composed by two interacting…
We show that the exact energy eigenvalues and eigenfunctions of the Schrodinger equation for charged particles moving in certain class of non-central potentials can be easily calculated analytically in a simple and elegant manner by using…
We discuss the arising of bound states solutions of the Schr\"odinger equation due to the presence of a Coulomb-type potential induced by the interaction between a moving electric quadrupole moment and a magnetic field. Furthermore, we…
Solitons on a finite a background, also called breathers, are solutions of the focusing nonlinear Schr\"odinger equation, which play a pivotal role in the description of rogue waves and modulation instability. The breather family includes…
The author suggests an approach based on the separation of total energy of multielectron systems into the semi-classical Coulomb part and the non-classical additional part. This approach allows on the one hand to simplify calculations and…
The supersymmetric approach in the form of second order intertwining relations is used to prove the exact solvability of two-dimensional Schrodinger equation with generalized two-dimensional Morse potential for $a_0=-1/2$. This…
The Nikiforov-Uvarov method is a simple, yet elegant and powerful method for solving second-order differential equations of generalized hypergeometric type. In the past, it has been used to solve many problems in quantum mechanics and…
Explicit solutions are obtained for a class of semilinear radial Schrodinger equations with power nonlinearities in multi-dimensions. These solutions include new similarity solutions and other new group-invariant solutions, as well as new…
We rigorously solve the time-independent Schr\"odinger equation for the Rosen-Morse type potential. By using the Nikiforov-Uvarov method, we obtain, in a systematic way, the complete solution of such equation, which includes the so-called…
Exact solutions to the d-dimensional Schroedinger equation, d\geq 2, for Coulomb plus harmonic oscillator potentials V(r)=-a/r+br^2, b>0 and a\ne 0 are obtained. The potential V(r) is considered both in all space, and under the condition of…
We show that there exist some intimate connections between three unconventional Schr\"odinger equations based on the use of deformed canonical commutation relations, of a position-dependent effective mass or of a curved space, respectively.…
The second-order partial derivatives of the Coulomb potential of a point charge can be regularized using the Coulomb potential of a charge of the oblate spheroidal shape that a moving rest-frame-spherical charge acquires by the Lorentz…
We distinguish two extreme classes of perturbation problems depending on the signs of second-order energy corrections and argue why it is generally much more probable to obtain a negative value of the same for any state in the standard…
Quasi-Exactly Solvable Schr\"odinger Equations occupy an intermediate place between exactly-solvable (e.g. the harmonic oscillator and Coulomb problems etc) and non-solvable ones. Their major property is an explicit knowledge of several…
Demonstrating the completeness of wave functions solutions of the radial Schrodinger equation is a very difficult task. Existing proofs, relying on operator theory, are often very abstract and far from intuitive comprehension. However, it…
An ab initio, three-dimensional quantum mechanical calculation has been performed for the time-evolution of continuum electrons in the fields of moving charges. Here the essential singularity associated with the diverging phase factor in…
Existence of degenerate stationary bound states with square integrable radial wave functions was proved when second-order equations are used with the effective potential of the Reissner-Nordstr\"{o}m (RN) field with two event horizons for…
Nonlinear second-order ordinary differential equations are common in various fields of science, such as physics, mechanics and biology. Here we provide a new family of integrable second-order ordinary differential equations by considering…
We numerically solve the Klein-Gordon equation at second order in cosmological perturbation theory in closed form for a single scalar field, describing the method employed in detail. We use the slow-roll version of the second order source…
We present a unified treatment of three cases of quasi-exactly solvable problems, namely, charged particle moving in Coulomb and magnetic fields, for both the Schr\"odinger and the Klein-Gordon case, and the relative motion of two charged…