Rigorous wave function for spin- composite particles

1968 ◽  
Vol 46 (7) ◽  
pp. 909-909
Author(s):  
Gerald Rosen
Keyword(s):  
Wave Function ◽  
Dirac Equation ◽  
Composite Particles ◽  
Spinor Wave Function ◽  
Relativistic Spin ◽  
Spinor Wave

A certain composite four-index quantity built up from three constituent spinor wave function solutions to the Dirac equation is shown to transform as a spinor and to satisfy the Dirac equation. This rigorous wave function is therefore associated with a composite relativistic spin-[Formula: see text] particle.

scholarly journals A study of elliptic biquaternionic angular momentum and Dirac equation

2021 ◽  
pp. 2150173
Author(s):  
Zülal Derin ◽  
Mehmet Ali Güngör
Keyword(s):  
Wave Function ◽  
Angular Momentum ◽  
Dirac Equation ◽  
Rotational Energy ◽  
Spinor Wave Function ◽  
Important Place ◽  
Relativistic Mass ◽  
Spinor Wave

In this paper, we deal with the Dirac equation and angular momentum, which have an important place in physics in terms of elliptic biquaternions. Thanks to the elliptic biquaternionic representation of angular momentum, we have expressed some useful mathematical and physical results. We obtain the solutions of the Dirac equation with the help of Dirac matrices with elliptic biquaternionic structure. Then, we have expressed the elliptic biquaternionic rotational Dirac equation. This equation could be interpreted as the combination of rotational energy and angular momentum of the particle and anti-particle. Therefore, we also discuss the elliptic biquaternionic form of rotational energy–momentum and of the relativistic mass. Further, we express the spinor wave function by elliptic biquaternions. Accordingly, we also show elliptic biquaternionic rotational Dirac energy–momentum solutions through this function.

Precise determination of the 4?-periodicity factor of a spinor wave function

1978 ◽  
Vol 29 (3) ◽  
pp. 281-284 ◽  
Author(s):  
H. Rauch ◽  
A. Wilfing ◽  
W. Bauspiess ◽  
U. Bonse
Keyword(s):  
Wave Function ◽  
Precise Determination ◽  
Spinor Wave Function ◽  
Spinor Wave

scholarly journals Exact Solution of the Curved Dirac Equation in Polar Coordinates: Master Function Approach

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
H. Panahi ◽  
L. Jahangiri
Keyword(s):  
Dirac Equation ◽  
Polar Coordinates ◽  
Invariance Property ◽  
Relativistic Energy ◽  
Spinor Wave Function ◽  
Shape Invariance ◽  
Second Order Differential Equations ◽  
Equations Of Mathematical Physics ◽  
Master Function ◽  
Spinor Wave

We show that the (2+1) curved Dirac equation in polar coordinates can be transformed into Schrodinger-like differential equation for upper spinor component. We compare this equation with the Schrodinger equation derived from shape invariance property of second order differential equations of mathematical physics. This formalism enables us to determine the electrostatic potential and relativistic energy in terms of master function and corresponding weight function. We also obtain the spinor wave function in terms of orthogonal polynomials.

Ansatz approach solution of the Duffin–Kemmer–Petiau equation for spin-1 particles with position-dependent mass in the presence of Kratzer-type potential

2014 ◽  
Vol 92 (12) ◽  
pp. 1565-1569 ◽  
Author(s):  
M.K. Bahar ◽  
F. Yasuk
Keyword(s):  
Wave Function ◽  
Scalar Potential ◽  
Energy Eigenvalues ◽  
Relativistic Spin ◽  
Ansatz Approach ◽  
Dependent Mass ◽  
Type Potential ◽  
Position Dependent Mass

The relativistic Duffin–Kemmer–Petiau equation for relativistic spin-1 particles with position-dependent mass in the presence of a vector Kratzer-type potential and the absence of a scalar potential is studied analytically. The energy eigenvalues and corresponding eigenfunctions are obtained using the wave function ansatz approach.

A solvable two-body Dirac equation in one space dimension

1991 ◽  
Vol 69 (7) ◽  
pp. 780-785 ◽  
Author(s):  
F. Dominguez-Adame ◽  
B. Méndez
Keyword(s):  
Wave Function ◽  
Dirac Equation ◽  
Space Dimension ◽  
Translational Motion ◽  
Effective Frequency ◽  
Klein Paradox ◽  
Independent Components ◽  
Dirac Particles ◽  
One Space Dimension

A solvable Hamiltonian for two Dirac particles interacting by instantaneous linear potentials in (1 + 1) dimensions is discussed. The system presents no Klein paradox even if the coupling is rather strong, so particles remain bound. The four independent components of the wave function describing the system resemble the nonrelativistic oscillator eigenfunctions. Although the Hamiltonian is not fully covariant, the effective frequency of the oscillator obeys a typical relativistic Doppler law. In contrast to the nonrelativistic treatment, eigenstates are intrinsically coupled with the overall translational motion of the system.

EXACT SOLUTIONS OF DIRAC EQUATION FOR A NEW SPHERICALLY ASYMMETRICAL SINGULAR OSCILLATOR

2010 ◽  
Vol 25 (33) ◽  
pp. 2849-2857 ◽  
Author(s):  
GUO-HUA SUN ◽  
SHI-HAI DONG
Keyword(s):  
Dirac Equation ◽  
Vector Potential ◽  
State Energy ◽  
Energy Levels ◽  
Scalar Potential ◽  
Bound State ◽  
Wave Functions ◽  
Bound State Energy ◽  
Exact Bound ◽  
Spinor Wave

In this work we solve the Dirac equation by constructing the exact bound state solutions for a mixing of scalar and vector spherically asymmetrical singular oscillators. This is done provided that the vector potential is equal to the scalar potential. The spinor wave functions and bound state energy levels are presented. The case V(r) = -S(r) is also considered.

scholarly journals J/ψ DECAY IN THE C3P0 MODEL

2012 ◽  
Vol 18 ◽  
pp. 200-203
Author(s):  
J. N. DE QUADROS ◽  
D. HADJIMICHEF
Keyword(s):  
Wave Function ◽  
Bound State ◽  
Pair Creation ◽  
Decay Rates ◽  
Composite Particles ◽  
Model C

The Fock-Tani representation, is a field theoretic formalism to treat problems involving both composite particles and their constituents. The application of the Fock-Tani transformation to a pair creation Hamiltonian produces the characteristic expansion in powers of the wave function. In lowest order of this expansion, we obtain the model known in the literature: the 3P0 model. In higher orders, the Corrected 3P0 model (C3P0) is obtained by introducing the bound state kernel. In this work, we use the C3P0 model to calculate the J/ψ decay rates in the following channels: ρ π, ω η, ω η′, K*+ K-, [Formula: see text], ϕ η, ϕ η′. We consider that the J/ψ is a mixture given by [Formula: see text].

scholarly journals Geometrical interpretation of the pilot wave theory and manifestation of spinor fields

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Mariya Iv. Trukhanova ◽  
Gennady Shipov
Keyword(s):  
Wave Theory ◽  
Geometrical Interpretation ◽  
Real Field ◽  
Spin Vector ◽  
Spinor Wave Function ◽  
Spinning Particle ◽  
Pilot Wave ◽  
Intrinsic Angular Momentum ◽  
Spinor Wave ◽  
Pilot Wave Theory

Abstract Using the hydrodynamical formalism of quantum mechanics for a Schrödinger spinning particle developed by Takabayashi, Vigier, and followers, which involves vortical flows, we propose a new geometrical interpretation of the pilot wave theory. The spinor wave in this interpretation represents an objectively real field, and the evolution of a material particle controlled by the wave is a manifestation of the geometry of space. We assume this field to have a geometrical nature, basing on the idea that the intrinsic angular momentum, the spin, modifies the geometry of the space, which becomes a manifold, represented as a vector bundle with a base formed by the translational coordinates and time, and the fiber of the bundle, specified at each point by the field of a tetrad $e^a_{\mu}$, forms from bilinear combinations of the spinor wave function. It has been shown that the spin vector rotates following the geodesic of the space with torsion, and the particle moves according to the geometrized guidance equation. This fact explains the self-action of the spinning particle. We show that the curvature and torsion of the spin vector line is determined by the space torsion of the absolute parallelism geometry.

Sign in / Sign up

Export Citation Format

Share Document