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In this paper we study the quantum dynamics of an electron/hole in a two-dimensional quantum ring within a spherical space. For this geometry, we consider a harmonic confining potential. Suggesting that the quantum ring is affected by the…

Quantum Physics · Physics 2020-01-08 A. L. Silva Netto , B. Farias , J. Carvalho , C. Furtado

It is shown that a class of approximate resonance solutions in the three-body problem under the Newtonian gravitational force are equivalent to quantized solutions of a modified Schr\"odinger equation for a wide range of masses that…

General Physics · Physics 2020-02-12 Edward Belbruno

We study the three-body Coulomb problem in two dimensions and show how to calculate very accurately its quantum properties. The use of a convenient set of coordinates makes it possible to write the Schr\"{o}dinger equation only using…

Quantum Physics · Physics 2009-11-07 L. Hilico , B. Grémaud , T. Jonckheere , N. Billy , D. Delande

We suggest a method for calculating electronic spectra in ordered and disordered semiconductor structures (superlattices) forming double quantum wells (QW). In our method, we represent the solution of Schr\"odinger equation for QW potential…

Materials Science · Physics 2022-04-13 Piotr Garbaczewski , Vladimir A. Stephanovich , Grzegorz Engel

We use the "tridiagonal representation approach" to solve the time-independent Schr\"odinger equation for bound states in a basis set of finite size. We obtain two classes of solutions written as finite series of square integrable functions…

Quantum Physics · Physics 2022-08-22 A. D. Alhaidari

This work investigates the motion of a non-relativistic charged particle within the spacetime of a global monopole. We introduce the Schr\"odinger equation to describe the particle's motion with two interactions by considering the Kratzer…

In this work, using the noncommutative integration method of linear differential equations, we obtain a complete set of solutions to the Schrodinger equation for a quantum asymmetric top in Euler angles. It is shown that the noncommutative…

Quantum Physics · Physics 2022-12-26 A. I. Breev , D. M. Gitman

The full analytical solution of the Schr\"{o}dinger equation for the hydrogen molecular ion $H_2^+$ (special case of the quantum tree-body problem with the Coulomb interaction) is obtained first. The solution shows that the total wave…

Quantum Physics · Physics 2015-08-18 A. V. Mitin

A simple real-space model for the electron wavefunction is suggested, based on a transverse wave with helicity, rotating at mc^2/h. The mapping of the real two-dimensional vector phasor to the complex plane permits this to satisfy the…

Quantum Physics · Physics 2007-05-23 Alan M. Kadin

We consider the inverse conductivity problem of identifying embedded objects in unbounded domains. The main tool is a set of special solutions to the Schroedinger equation, the complex spherical waves, which are constructed by a Carleman…

Analysis of PDEs · Mathematics 2009-11-11 Mikko Salo , Jenn-Nan Wang

We present the analytical solution of the wavefunction and energy dispersion of armchair graphene nanoribbons (GNRs) based on the tight-binding approximation. By imposing hard-wall boundary condition, we find that the wavevector in the…

Mesoscale and Nanoscale Physics · Physics 2015-06-25 Huaixiu Zheng , Zhengfei Wang , Tao Luo , Qinwei Shi , Jie Chen

Analytical solutions of the Klein-Gordon equation are obtained by reducing the radial part of the wave equation to a standard form of a second order differential equation. Differential equations of this standard form are solvable in terms…

Quantum Physics · Physics 2015-06-18 Huseyin Akcay , Ramazan Sever

The Schr\"odinger equation in a square or rectangle with hard walls is solved in every introductory quantum mechanics course. Solutions for other polygonal enclosures only exist in a very restricted class of polygons, and are all based on a…

Computational Physics · Physics 2022-06-10 M. F. C. Martins Quintela , J. M. B. Lopes dos Santos

The electromagnetic interaction with quarks is investigated through a relativistic, electromagnetic gauge-invariant treatment. Gluon dressing of the quark-photon vertex and the quark self-energy functions is described by the inhomogeneous…

Nuclear Theory · Physics 2009-09-25 Michael R. Frank

The Schr\"odinger equation relates the electron wavefunction and the electric potential, which are emergent physical quantities. At that emergent level, the Schr\"odinger equation is either postulated as a principle of quantum physics or…

Quantum Physics · Physics 2022-12-27 Spyros Efthimiades

We propose an approach to quantize discrete networks (graphs with discrete edges). We introduce a new exact solution of discrete Schrodinger equation that is used to write the solution for quantum graphs. Formulation of the problem and…

Quantum Physics · Physics 2024-11-22 M. Akramov , C. Trunk , J. Yusupov , D. Matrasulov

An alternative approximation scheme has been used in solving the Schrodinger equation for the exponential-cosine-screened Coulomb potential. The bound state energ\i es for various eigenstates and the corresponding wave functions are…

Quantum Physics · Physics 2007-05-23 Sameer M. Ikhdair , Ramazan Sever

We present realistic simulations of quantum confinement effects in ballistic graphene quantum dots with linear dimensions of 10 to 40 nm. We determine wavefunctions and energy level statistics in the presence of disorder resulting from edge…

Mesoscale and Nanoscale Physics · Physics 2009-03-18 F. Libisch , C. Stampfer , J. Burgdörfer

An exact quantization rule for the Schr\"{o}dinger equation is presented. In the exact quantization rule, in addition to $N\pi$, there is an integral term, called the quantum correction. For the exactly solvable systems we find that the…

Computational Physics · Physics 2015-06-26 Zhong-Qi Ma , Bo-Wei Xu

For the first time, the general nonlinear Schr\"odinger equation is investigated, in which the chromatic dispersion and potential are specified by two arbitrary functions. The equation in question is a natural generalization of a wide class…

Exactly Solvable and Integrable Systems · Physics 2024-12-03 Andrei D. Polyanin , Nikolay A. Kudryashov