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Bound states of the power-law and logarithmic potentials are calculated using a generalized pseudospectral method. The solution of the single-particle Schr\"odinger equation in a nonuniform and optimal spatial discretization offers accurate…

Quantum Physics · Physics 2015-06-16 Amlan K. Roy

A systematic procedure to study one-dimensional Schr\"odinger equation with a position-dependent effective mass (PDEM) in the kinetic energy operator is explored. The conventional free-particle problem reveals a new and interesting…

Quantum Physics · Physics 2009-11-10 B. Bagchi , P. Gorain , C. Quesne , R. Roychoudhury

In this work, we obtained analytical bound state solution of the Schr\"odinger equation with Manning Rosen plus exponential Yukawa Potential using parametric Nikiforov-Uvarov method (NU). We obtained the normalized wave function in terms of…

The Schr\"{o}dinger equation is solved exactly for some well known potentials. Solutions are obtained reducing the Schr\"{o}dinger equation into a second order differential equation by using an appropriate coordinate transformation. The…

Quantum Physics · Physics 2019-12-06 Cevdet Tezcan , Ramazan Sever

We obtain the quantized momentum eigenvalues, $P_n$ , and the momentum eigenstates for the space-like Schr\"odinger equation, the Feinberg-Horodecki equation, with the general potential which is constructed by the temporal counterpart of…

Quantum Physics · Physics 2020-07-29 Mahmoud Farout , Ahmed Bassalat , Sameer M. Ikhdair

We solve the one-dimensional Schr\"odinger equation for the bound states of two potential models with a rich structure as shown by their "spectral phase diagram". These potentials do not belong to the well-known class of exactly solvable…

Quantum Physics · Physics 2022-09-09 A. D. Alhaidari , I. A. Assi

We prove the existence of a class of orbitally stable bound state solutions to nonlinear Schr\"odinger equations with super-quadratic confinement in two and three spatial dimensions. These solutions are given by time-dependent rotations of…

Analysis of PDEs · Mathematics 2024-11-28 Irina Nenciu , Xiaoan Shen , Christof Sparber

Necessary and sufficient conditions for existence of boundary value problem of Schrodinger equation are obtained in linear and nonlinear cases. Periodic analytical solutions are represented using generalized Green's operator

Mathematical Physics · Physics 2012-09-04 A. A. Boichuk , A. A. Pokutnyi

Schr\"odinger-type eigenvalue problems are ubiquitous in theoretical physics, with quantum-mechanical applications typically confined to cases for which the eigenfunctions are required to be normalizable on the real axis. However, seeking…

High Energy Physics - Theory · Physics 2025-08-01 Björn Garbrecht , Nils Wagner

The eigenstates of a real or complex cubic anharmonic oscillator are investigated using original and alternative methods. The procedure consists of determining global solutions of the Schr\"odinger equation that comply with the pertinent…

Quantum Physics · Physics 2016-01-13 E. M. Ferreira , J. Sesma

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…

Quantum Physics · Physics 2008-01-28 Ramazan Sever , Mahmut Bucurgat , Cevdet Tezcan , Ozlem Yesiltas

The treatment of the time-independent Schrodinger equation in real-space is an indispensable part of introductory quantum mechanics. In contrast, the Schrodinger equation in momentum space is an integral equation that is not readily…

Computational Physics · Physics 2015-05-14 William A. Karr , Christopher R. Jamell , Yogesh N. Joglekar

The polynomial solution of the Schrodinger equation for the Pseudoharmonic potential is found for any arbitrary angular momentum $l$. The exact bound-state energy eigenvalues and the corresponding eigen functions are analytically…

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

A duality between an electrostatic problem in a three dimensional world and a quantum mechanical problem in a one dimensional world which allows one to obtain the ground state solution of the Schr\"odinger equation by using electrostatic…

Quantum Physics · Physics 2021-07-13 G. Gonzalez

We obtain the exact energy spectrum of nonuniform mass particles for a collection of Hamiltonians in a three-dimensional approach to a quantum dot. By considering a set of generalized Schr\"odinger equations with different orderings between…

Mesoscale and Nanoscale Physics · Physics 2023-11-27 R. M. Lima , H. R. Christiansen

This paper presents an accurate highly efficient method for solving the bound states in the one-dimensional Schr\"odinger equation with an arbitrary potential. We show that the bound state energies of a general potential well can be…

Quantum Physics · Physics 2019-09-12 Carlos Ramírez , Fernanda H. González , César G. Galván

We revisit the model of a system made up of a Brownian quantum oscillator under the influence of an external classical force and linearly coupled to an environment made up of many quantum oscillators at zero or finite temperature. We show…

Quantum Physics · Physics 2007-05-23 C. H. Fleming , B. L. Hu , Albert Roura

On the contrary to the common intuition, which suggests that a steep expulsive potential makes quantum states widely delocalized, we demonstrate that one- and two-dimensional (1D and 2D) Schroedinger equations, which include expulsive…

Quantum Physics · Physics 2026-04-28 H. Sakaguchi , B. A. Malomed , A. C. Aristotelous , E. G. Charalampidis

The homogeneous Lippmann-Schwinger integral equation is solved in momentum space by using confining potentials. Since the confining potentials are unbounded at large distances, they lead to a singularity at small momentum. In order to…

High Energy Physics - Phenomenology · Physics 2011-11-10 M. R. Hadizadeh , Lauro Tomio

In this paper, we consider the existence, orbital stability/instability and regularity of bound state solutions to nonlinear Schr\"odinger equations with super-quadratic confinement in two and three spatial dimensions for the mass…

Analysis of PDEs · Mathematics 2025-10-14 Tianxiang Gou , Xiaoan Shen