Analytical Solution of the Schrödinger Equation for the Linear Combination of the Manning–Rosen and the Class of Yukawa Potentials

2022 ◽  
Author(s):  
G. A. Bayramova
Keyword(s):  
Analytical Solution ◽  
Schrödinger Equation ◽  
Linear Combination ◽  
Schrodinger Equation ◽  
Yukawa Potentials

Three and Four Centre Oscillators and Their Application in Nuclear Physics

1974 ◽  
Vol 29 (7) ◽  
pp. 1003-1010 ◽  
Author(s):  
Peter Bergmann ◽  
Hans-Joachim Scheefer
Keyword(s):  
Analytical Solution ◽  
Schrödinger Equation ◽  
Nuclear Physics ◽  
Schrodinger Equation ◽  
Numerical Procedure ◽  
Orthogonal Basis ◽  
Two Dimensional ◽  
Schmidt's Method ◽  
Symmetry Properties

The extension of the nuclear two-centre-oscillator to three and four centres is investigated. Some special symmetry-properties are required. In two cases an analytical solution of the Schrödinger equation is possible. A numerical procedure is developed which enables the diagonalization of the Hamiltonian in a non-orthogonal basis without applying Schmidt's method of orthonormalization. This is important for calculations of arbitrary two-dimensional arrangements of the centres.

Analytical solution of the Schrödinger equation for an electron confined in a triangle-shaped quantum well

2003 ◽  
Vol 66 (1-4) ◽  
pp. 39-45 ◽  
Author(s):  
Peter N Gorley ◽  
Yuri V Vorobiev ◽  
Jesús González-Hernández ◽  
Paul P Horley
Keyword(s):  
Analytical Solution ◽  
Schrödinger Equation ◽  
Quantum Well ◽  
Schrodinger Equation

HYPERSPHERICAL APPROACH TO STUDY THE SCHRÖDINGER EQUATION FOR AN N-PARTICLE SYSTEM

2009 ◽  
Vol 18 (07) ◽  
pp. 1497-1502
Author(s):  
H. HASSANABADI ◽  
A. A. RAJABI ◽  
M. M. SHOJAEI
Keyword(s):  
Analytical Solution ◽  
Schrödinger Equation ◽  
Excited States ◽  
Ground State ◽  
Schrodinger Equation ◽  
Particle System ◽  
Exact Analytical Solution ◽  
Hyperspherical Approach

In the present work we give an exact analytical solution of the Schrödinger equation for an N-particle system by using the hyperspherical approach, in the presence of the hypercentral potential of form V(R) = a1R2+b1R-4+c1R-6 for both the ground state and the excited states.

Non-relativistic s-wave binding energies of Λ-particle in hypernuclei

2016 ◽  
Vol 31 (14) ◽  
pp. 1650084 ◽  
Author(s):  
A. Armat ◽  
H. Hassanabadi
Keyword(s):  
Experimental Data ◽  
Binding Energy ◽  
Analytical Solution ◽  
Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Binding Energies ◽  
S Wave ◽  
Ground State Binding Energy ◽  
Type Interaction

In this work, the ground state binding energy of [Formula: see text]-particle in hypernuclei is investigated by using analytical solution of non-relativistic Schrödinger equation in the presence of a generalized Woods–Saxon-type interaction. The comparison with the experimental data is motivating.

scholarly journals Breve argumentación didáctica de la mecánica cuántica de muchos cuerpos

Respuestas ◽  
2017 ◽  
Vol 22 (1) ◽  
pp. 29
Author(s):  
Cristian Andrés Aguirre-Téllez ◽  
José Barba-Ortega
Keyword(s):  
Quantum Mechanics ◽  
Analytical Solution ◽  
Schrödinger Equation ◽  
Analytical Method ◽  
Schrodinger Equation ◽  
Quantum Systems ◽  
The Self ◽  
Self Consistent ◽  
El Sistema ◽  
Self Consistent Field

El problema general en mecánica cuántica está basado en la solución de una ecuación en valores propios de un operador dado (en una representación adecuada), generalmente  dicho operador es el Hamiltoniano que da cuenta de la interacción energética (salvo que dependa del tiempo) del sistema en cuestión. La solución de la ecuación de Schrödinger permite escribir el comportamiento dinámico del sistema sometido a ciertas restricciones. Sin embargo, la solución analítica de esta ecuación es viable solo en sistemas simples, cuando el sistema se describe desde la interacción de muchas partículas (problema electrónico-base de la construcción de sistemas cuánticos complejos aplicable a la descripción de moléculas, sólidos y sistemas cuánticos interactuantes en general.) la solución de la ecuación de Schrödinger del sistema no se puede realizar vía método analítico; con lo cual existe una forma más global de enfrentar dicho problema, el método auto consistente; mediante el cual se puede solucionar sistemas complejos de muchos cuerpos. Es así que en el presente paper presentamos una comparación entre el sistema auto consistente y algunas variantes que existen, con el método analítico en sistemas demuchos cuerpos y como opera dicho método, esto aplicado a un problema de dos cuerpos con interacción Coulombiana, ya que este problema presenta solución analítica y ha sido extensamente estudiado; esto con la finalidad de que los estudiantes interesados en la materia comprendan como se abordan problemas vía métodos auto consistentes y como opera este método, ya que en la literatura pocas veces se presenta el algoritmo de solución mediante este método.Palabras clave: Mecánica Cuántica, Método Auto-Consistente, problema de dos cuerpos.AbstractThe general problem in quantum mechanics is based on the solution of an equation in eigenvalues of a given operator (in a suitable representation), generally said operator is the Hamiltonian that accounts for the energy interaction (unless it depends on the time) of the system in question. The solution of the Schrodinger equation allows writing the dynamic behavior of the system subject to certain restrictions. however, the analytical solution of this equation is feasible only in simple systems, when the system is described from the interaction of many particles (electronic problem- basis of the construction of complex quantum systems applicable to the description of molecules, solids and interacting quantum systems in general.), the solution of the Schrödinger equation of the system can´t be performed via analytical method; with which there is a more global way of facing this problem, the self-consistent method; through which complex systems of many bodies can be solved. thus, in the present paper we present a comparison between the self-consistent system and some variants that exist, with the analytical method in systems of many bodies and how this method operates, this applied to a problem of two bodies with Coulombian interaction, since this problem presents an analytical solution and has been extensively studied; this in order that students interested in the subject understand how problems are addressed through self-consistent methods and how this method operates, since in the literature rarely the solution algorithm is presented by this method.Keywords: Quantum mechanics, Self Consistent Field, Two body problem.

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