EXACT SOLUTIONS OF SCHRODINGER'S EQUATION FOR SPIN SYSTEMS IN A CLASS OF TIME DEPENDENT MAGNETIC FIELDS: II

1992 ◽  
Vol 06 (20) ◽  
pp. 1255-1261 ◽  
Author(s):  
M. J. TAHMASEBI ◽  
Y. SOBOUTI
Keyword(s):  
Exact Solutions ◽  
Variable Magnetic Field ◽  
Spin Systems ◽  
Level System ◽  
Schrödinger’S Equation ◽  
Integrating Factor ◽  
Exactly Solvable ◽  
Wave Forms ◽  
Schrödinger's Equation ◽  
Factor Technique

The case of a quantum two-level system coupled to a time variable magnetic field is investigated. The Schrodinger equation pertaining to the system is reduced to a second order linear equation in time and its solutions are sought by an integrating factor technique. A differential equation for the integrating factor and, therefrom, a criterion for fields leading to exact solutions are derived. The formalism is capable of giving a wide variety of closed form radio frequency (RF) wave forms for which Schrodinger's equation is exactly solvable.

EXACT SOLUTIONS OF SCHRODINGER’S EQUATION FOR SPIN SYSTEMS IN A CLASS OF TIME-DEPENDENT MAGNETIC FIELDS

1991 ◽  
Vol 05 (29) ◽  
pp. 1919-1924 ◽  
Author(s):  
M.J. TAHMASEBI ◽  
Y. SOBOUTI
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Exact Solutions ◽  
Spin System ◽  
Schrodinger Equation ◽  
Unitary Transformation ◽  
Variable Magnetic Field ◽  
Spin Systems ◽  
Time Variable ◽  
Time Dependent

A spin system in a time variable magnetic field is considered. For certain fields there exists a frame in which the Hamiltonian becomes static. The criterion for such fields is derived. The unitary transformation that accomplishes this task is obtained and the underlying Schrodinger equation is solved exactly.

scholarly journals Exact solutions to the perturbed nonlinear Schrödinger's equation with Kerr law nonlinearity by using the first integral method

2011 ◽  
Vol 16 (3) ◽  
pp. 332-339 ◽  
Author(s):  
Hossein Moosaei ◽  
Mohammad Mirzazadeh ◽  
Ahmet Yildirim
Keyword(s):  
Exact Solutions ◽  
Integral Method ◽  
First Integral ◽  
First Integral Method ◽  
Schrödinger’S Equation ◽  
Kerr Law ◽  
Kerr Law Nonlinearity ◽  
Schrödinger's Equation ◽  
Nonlinear Schrodinger’S Equation ◽  
Nonlinear Schrödinger’S Equation

The first integral method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. In this paper, the first integral method is used to construct exact solutions of the perturbed nonlinear Schrodinger’s equation (NLSE) with Kerr law nonlinearity. It is shown that the proposed method is effective and general.

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