Covariant two-particle wave functions for model quasipotentials that admit exact solutions. II. Solutions in the relativistic configuration representation

1983 ◽  
Vol 55 (1) ◽  
pp. 330-338 ◽  
Author(s):  
V. N. Kapshai ◽  
N. B. Skachkov
Keyword(s):  
Exact Solutions ◽  
Wave Functions ◽  
Configuration Representation ◽  
Relativistic Configuration ◽  
Relativistic Configuration Representation

Partial Quasipotential Equations in the Relativistic Configuration Representation

2018 ◽  
Vol 60 (10) ◽  
pp. 1696-1704 ◽  
Author(s):  
V. N. Kapshai ◽  
S. I. Fialka
Keyword(s):  
Configuration Representation ◽  
Relativistic Configuration ◽  
Relativistic Configuration Representation

On Threshold Resummation S-Factor for a System of Two Relativistic Spinor Particles with Arbitrary Masses

2020 ◽  
Vol 23 (4) ◽  
pp. 449-460
Author(s):  
Yu. D. Chernichenko ◽  
L. P. Kaptari ◽  
O. P. Solovtsova
Keyword(s):  
Composite System ◽  
Hamiltonian Formulation ◽  
Quantum Field ◽  
Quasipotential Approach ◽  
Threshold Resummation ◽  
S Factor ◽  
Configuration Representation ◽  
Relativistic Configuration ◽  
The Difference ◽  
Relativistic Configuration Representation

We present a new threshold resummation S-factor obtained for a composite system of two relativistic spin 1/2 particles of arbitrary masses interacting via a Coulomb-like chromodynamical potential. The analysis is performed in the framework of a relativistic quasipotential approach in the Hamiltonian formulation of the quantum field theory in the relativistic configuration representation. The pseudoscalar, vector, and pseudovector systems are considered. The difference in the behavior of the S-factor for these cases is discussed. A connection between the new and the previously obtained S-factors for spinless particles of arbitrary masses and relativistic spinor particles of equal masses is established.

Exact solutions of a quartic potential

2019 ◽  
Vol 34 (26) ◽  
pp. 1950208 ◽  
Author(s):  
Qian Dong ◽  
Guo-Hua Sun ◽  
M. Avila Aoki ◽  
Chang-Yuan Chen ◽  
Shi-Hai Dong
Keyword(s):  
Exact Solutions ◽  
Quantum System ◽  
Analytical Solutions ◽  
Wave Functions ◽  
Negative Potential ◽  
Potential Parameter ◽  
Real Numbers ◽  
Quartic Potential ◽  
Heun Functions ◽  
Potential Parameters

We find that the analytical solutions to quantum system with a quartic potential [Formula: see text] (arbitrary [Formula: see text] and [Formula: see text] are real numbers) are given by the triconfluent Heun functions [Formula: see text]. The properties of the wave functions, which are strongly relevant for the potential parameters [Formula: see text] and [Formula: see text], are illustrated. It is shown that the wave functions are shrunk to the origin for a given [Formula: see text] when the potential parameter [Formula: see text] increases, while the wave peak of wave functions is concaved to the origin when the negative potential parameter [Formula: see text] increases or parameter [Formula: see text] decreases for a given negative potential parameter [Formula: see text]. The minimum value of the double well case ([Formula: see text]) is given by [Formula: see text] at [Formula: see text].

EXACT SOLUTIONS OF THE SCHRÖDINGER EQUATION WITH SPHERICALLY SYMMETRIC OCTIC POTENTIAL

2012 ◽  
Vol 27 (20) ◽  
pp. 1250112 ◽  
Author(s):  
DAVIDS AGBOOLA ◽  
YAO-ZHONG ZHANG
Keyword(s):  
Schrödinger Equation ◽  
Exact Solutions ◽  
Closed Form ◽  
Schrodinger Equation ◽  
Wave Functions ◽  
Spherically Symmetric ◽  
Algebraic Equations ◽  
Potential Parameters

We present exact solutions of the Schrödinger equation with spherically symmetric octic potential. We give closed-form expressions for the energies and the wave functions as well as the allowed values of the potential parameters in terms of a set of algebraic equations.

scholarly journals EXACT SOLUTIONS OF THE DIRAC EQUATION FOR MODIFIED COULOMBIC POTENTIALS

2000 ◽  
Vol 15 (27) ◽  
pp. 4355-4360
Author(s):  
ANTONIO SOARES DE CASTRO ◽  
JERROLD FRANKLIN
Keyword(s):  
Dirac Equation ◽  
Exact Solutions ◽  
Linear Combination ◽  
Ground State ◽  
Wave Functions ◽  
Orbital State ◽  
Lorentz Scalar ◽  
Scalar Part

Exact solutions are found for the Dirac equation for a combination of Lorentz scalar and vector Coulombic potentials with additional non-Coulombic parts. An appropriate linear combination of Lorentz scalar and vector non-Coulombic potentials, with the scalar part dominating, can be chosen to give exact analytic Dirac wave functions. The method works for the ground state or for the lowest orbital state with l=j-½, for any j.

Exact solutions to solitonic profile mass Schrödinger problem with a modified Pöschl–Teller potential

2016 ◽  
Vol 31 (04) ◽  
pp. 1650017 ◽  
Author(s):  
Shishan Dong ◽  
Qin Fang ◽  
B. J. Falaye ◽  
Guo-Hua Sun ◽  
C. Yáñez-Márquez ◽  
...  
Keyword(s):  
Wave Function ◽  
Exact Solutions ◽  
Ground State ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Wave Functions ◽  
Numerical Calculations ◽  
Potential Parameter ◽  
Heun Functions ◽  
Single Well

We present exact solutions of solitonic profile mass Schrödinger equation with a modified Pöschl–Teller potential. We find that the solutions can be expressed analytically in terms of confluent Heun functions. However, the energy levels are not analytically obtainable except via numerical calculations. The properties of the wave functions, which depend on the values of potential parameter [Formula: see text] are illustrated graphically. We find that the potential changes from single well to a double well when parameter [Formula: see text] changes from minus to positive. Initially, the crest of wave function for the ground state diminishes gradually with increasing [Formula: see text] and then becomes negative. We notice that the parities of the wave functions for [Formula: see text] also change.

EXACT QUANTUM STATES OF AN INVERTED PENDULUM UNDER TIME-DEPENDENT GRAVITATION

2004 ◽  
Vol 19 (24) ◽  
pp. 4165-4172 ◽  
Author(s):  
I. A. PEDROSA ◽  
I. GUEDES
Keyword(s):  
Exact Solutions ◽  
Inverted Pendulum ◽  
Quantum States ◽  
Wave Functions ◽  
Time Dependent ◽  
Invariant Method ◽  
Exact Quantum ◽  
Generalized Time

We discuss the Lewis and Riesenfeld invariant method for cases where the invariant has continuous eigenvalues and use it to find the Schrödinger wave functions of an inverted pendulum under time-dependent gravitation. As a particular case, we consider an inverted pendulum with exponentially increasing mass and constant gravitation. We also obtain the exact solutions for a generalized time-dependent inverted pendulum.

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