Non-Lie ansatzen and exact solutions of a nonlinear spinor equation

1990 ◽  
Vol 42 (7) ◽  
pp. 851-855 ◽  
Author(s):  
V. I. Fushchich ◽  
R. Z. Zhdanov
Keyword(s):  
Exact Solutions ◽  
Nonlinear Spinor ◽  
Spinor Equation

Symmetry and exact solutions of nonlinear spinor equations

1989 ◽  
Vol 172 (4) ◽  
pp. 123-174 ◽  
Author(s):  
W.I. Fushchich ◽  
R.Z. Zhdanov
Keyword(s):  
Exact Solutions ◽  
Nonlinear Spinor

Many-Body-Systems and Exciton Model in New-Tamm-Dancoff- Formulation

1975 ◽  
Vol 30 (11) ◽  
pp. 1333-1346
Author(s):  
F. Wahl
Keyword(s):  
Many Body ◽  
Field Equations ◽  
Solid State Physics ◽  
Nonlinear Spinor ◽  
Exciton Model ◽  
Fundamental Field ◽  
Spinor Equation ◽  
Many Body Systems ◽  
Infinite Linear System ◽  
Infinite Linear

The NTD-method is a procedure to compute differences of eigenvalues in quantum mechanical problems: ωαβ=λα-λβ.It is an instruction to transform and truncate an infinite linear system of eigenvalue equations ω τk= Akm τm which is derived with the aid of fundamental field equations or corresponding Hamilton-operators, as e.g. with Heisenberg's nonlinear spinor equation. In this paper we want to test the NTD-method for a many-body-model in solid state physics. We elaborate on the physical and mathematical aspects by choosing a suitable transformation τ → φ = C τ to get a new linear 1 system ω φk= Bkk+2iφk+2i which permits a truncation to evaluate approximation of states. The efficiency of this method is demonstrated by treating a two-body-system in presence of polarisation quanta, known as exciton model

Eine klassische Feldtheorie für die innere Struktur des Elektrons / A Classical Field Theory Describing the Inner Structure of an Electron

1970 ◽  
Vol 25 (7) ◽  
pp. 985-992
Author(s):  
Erwin Kasper
Keyword(s):  
Center Of Mass ◽  
Classical Field Theory ◽  
External Electromagnetic Field ◽  
Classical Field ◽  
Laboratory System ◽  
Spin Tensor ◽  
Tensor Equation ◽  
Nonlinear Spinor ◽  
Spinor Equation ◽  
Heisenberg's Uncertainty Principle

A theory is given which permits a connection between an inner structure of an electron and the motion of its center of mass obeying Dirac's equation. In order to describe inner properties of the particle a classical nonlinear spinor equation is derived from a Lagrangian. There exist rotational symmetric solutions which are simultaneously finite, stationary, normalizable and strongly localisated, and which yield the mass at rest, the spin and the magnetic moment of the particle in a correct manner. Since these solutions are in contradiction to Heisenberg's uncertainty principle the calculated properties cannot be directly observed in the laboratory system. Therefore an eight-dimensional configuration space is introduced containing the laboratory system and the center-of-masssystem. In this space the wave equation is formulated as a nonlinear differential equation for a spin tensor of second order. If the interaction with an external electromagnetic field is very weak a separation of this tensor equation into the nonlinear spinor equation mentioned above and into Dirac's equation is possible. Observable quantities in the laboratory system can be obtained by integration over the inner coordinates

Sign in / Sign up

Export Citation Format

Share Document