scholarly journals Solutions for a q-generalized Schrödinger equation of entangled interacting particles

2015 ◽  
Vol 429 ◽  
pp. 35-44 ◽  
Author(s):  
L.G.A. Alves ◽  
H.V. Ribeiro ◽  
M.A.F. Santos ◽  
R.S. Mendes ◽  
E.K. Lenzi
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Interacting Particles ◽  
Generalized Schrödinger Equation

The interaction representation in the quantum theory of fields

1950 ◽  
Vol 201 (1065) ◽  
pp. 284-296 ◽  
Keyword(s):  
Quantum Theory ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Unitary Transformation ◽  
Present Theory ◽  
Point Of View ◽  
Field Equations ◽  
Generalized Schrödinger Equation ◽  
Invariant Interaction ◽  
Theory Of Fields

The interaction representation has recently been introduced into the quantum theory of fields by Tomonaga and Schwinger. Applications of the theory to interacting meson-photon fields have led to apparent difficulties in determining invariant interaction Hamiltonians. Another troublesome feature is the necessity of verifying the integrability conditions of the so-called generalized Schrödinger equation. In the present paper the theory of the interaction representation is presented from a different point of view. It is shown that if two field operators with the same transformation character satisfy two different field equations, there is a unique unitary transformation connecting the field variables on any space-like surface given such a correspondence on one given space-like surface. A differential equation for determining this unique unitary transformation is found which is the analogue of Tomonaga’s generalized Schrödinger equation. This gives directly and simply an invariant interaction Hamiltonian and renders unnecessary the explicit verification of the integrability of the Schrödinger equation, since this is known to have a unique solution. To illustrate the simplification introduced by the present theory, the interaction Hamiltonian for the interacting scalar meson-photon fields is calculated. The result is the same as that obtained by Kanesawa & Tomonaga, but it is obtained by a straightforward calculation without the need to add terms to make the Hamiltonian an invariant.

BIFURCATIONS OF TRAVELING WAVE SOLUTIONS AND EXACT SOLUTIONS FOR THE GENERALIZED SCHRÖDINGER EQUATION

2011 ◽  
Vol 21 (09) ◽  
pp. 2623-2628
Author(s):  
JIANMING ZHANG ◽  
SHUMING LI
Keyword(s):  
Schrödinger Equation ◽  
Soliton Solution ◽  
Schrodinger Equation ◽  
Traveling Wave Solutions ◽  
Dark Soliton ◽  
Periodic Wave ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Generalized Schrödinger Equation ◽  
Bright Soliton Solution

Using the method of dynamical systems for the generalized Schrödinger equation, the bright soliton solution, dark soliton solution, uncountably infinite many periodic wave solutions and breaking bounded wave solutions are obtained. Exact explicit parametric representations of the bounded traveling solutions are given. To guarantee the existence of the above solutions, all parameter conditions are determined.

scholarly journals An Analytic Evolutionary Algorithm To Compute Higher-Order Solutions For Model Equation

2021 ◽  
Author(s):  
Bang-Qing Li ◽  
Yu-Lan Ma
Keyword(s):  
Schrödinger Equation ◽  
Evolutionary Algorithm ◽  
Lower Order ◽  
Schrodinger Equation ◽  
Model Equation ◽  
Evolutionary Computing ◽  
Higher Order ◽  
Third Order ◽  
Generalized Schrödinger Equation ◽  
Basic Features

Abstract In this work, by introducing Darboux operator in evolutionary computing frame, we propose a novel analytic evolutionary algorithm to obtain exact higher-order iteration solutions for model equation. We construct the first-, second- and third-order solutions of a generalized Schrödinger equation by applying this algorithm. The higher-order solutions not only retain the basic features of the lower-order cases, but also become more abundant than the lower-order cases.

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