GRASSMANN WAVE FUNCTIONS AND INTRINSIC SPIN

By associating spin angular momentum with Sp(2) transformations on two Grassmann coordinates, we show how one may formulate spinor wave functions in complete analogy to spherical harmonics for orbital momentum. The relativistic generalization requires a doubling of Grassmann coordinates and a connection may be established with the Dirac equation.

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

Modern Physics Letters A ◽

10.1142/s0217732310033785 ◽

2010 ◽

Vol 25 (33) ◽

pp. 2849-2857 ◽

Cited By ~ 18

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.

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Pseudospin and Spin Symmetric Solutions of the Dirac Equation: Hellmann Potential,Wei–Hua Potential, Varshni Potential

Zeitschrift für Naturforschung A ◽

10.5560/zna.2014-0007 ◽

2014 ◽

Vol 69 (3-4) ◽

pp. 163-172 ◽

Cited By ~ 5

Author(s):

Altuğ Arda ◽

Ramazan Sever

Keyword(s):

Dirac Equation ◽

Analytical Solutions ◽

Energy Eigenvalue ◽

Wave Functions ◽

K Value ◽

Energy Eigenvalues ◽

Approximate Analytical Solutions ◽

Hellmann Potential ◽

Uvarov Method ◽

Spinor Wave

Approximate analytical solutions of the Dirac equation are obtained for the Hellmann potential, the Wei-Hua potential, and the Varshni potential with any k-value for the cases having the Dirac equation pseudospin and spin symmetries. Closed forms of the energy eigenvalue equations and the spinor wave functions are obtained by using the Nikiforov-Uvarov method and some tables are given to see the dependence of the energy eigenvalues on different quantum number pairs (n;κ).

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SOLUTION OF THE DIRAC EQUATION WITH NONCENTRAL THREE-VECTOR POTENTIAL

Modern Physics Letters A ◽

10.1142/s0217732306019049 ◽

2006 ◽

Vol 21 (07) ◽

pp. 581-592 ◽

Cited By ~ 2

Author(s):

A. D. ALHAIDARI

Keyword(s):

Energy Spectrum ◽

Dirac Equation ◽

Vector Potential ◽

Radial Component ◽

Wave Functions ◽

Relativistic Energy ◽

Dirac Oscillator ◽

Spherical Coordinates ◽

The One ◽

Spinor Wave

We introduce coupling to three-vector potential in the (3+1)-dimensional Dirac equation. The potential is noncentral (angular-dependent) such that the Dirac equation separates completely in spherical coordinates. The relativistic energy spectrum and spinor wave functions are obtained for the case where the radial component of the vector potential is proportional to 1/r. The coupling presented in this work is a generalization of the one which was introduced by Moshinsky and Szczepaniak for the Dirac-oscillator problem.

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Pseudo-spin Symmetry in Dirac-Four-Parameter Diatomic Problem Coupled with a Coulomb-like Tensor potential

BIBECHANA ◽

10.3126/bibechana.v8i0.4879 ◽

2012 ◽

Vol 8 ◽

pp. 23-30

Author(s):

Mahdi Eshghi

Keyword(s):

Energy Spectrum ◽

Dirac Equation ◽

State Energy ◽

Spin Symmetry ◽

Bound State ◽

Wave Functions ◽

Bound State Energy ◽

Tensor Potential ◽

Uvarov Method ◽

Spinor Wave

In this work, we use the parametric generalization of the Nikiforov-Uvarov method to obtain the relativistic bound state energy spectrum and the corresponding spinor wave-functions for four-parameter diatomic potential coupled with a Coulomb-like tensor under the condition of the pseudo-spin symmetry. Also, some numerical results have given.Keywords: Dirac equation; four-parameter diatomic potential; Coulomb-like tensorDOI: http://dx.doi.org/10.3126/bibechana.v8i0.4879BIBECHANA 8 (2012) 23-30

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A study of elliptic biquaternionic angular momentum and Dirac equation

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887821501735 ◽

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.

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XII.—Reciprocity. Part IV: Spinor Wave Functions

Proceedings of the Royal Society of Edinburgh ◽

10.1017/s0370164600020149 ◽

1940 ◽

Vol 60 (2) ◽

pp. 147-163 ◽

Cited By ~ 4

Author(s):

Klaus Fuchs

Keyword(s):

Dirac Equation ◽

Wave Functions ◽

Spinor Wave

This paper is the continuation of the papers by Born (1939, Part I) and by Born and myself (1940, Parts II and III). Here the theory is extended to the case of spinor wave functions satisfying the Dirac equation.

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Introduction of spin torques

10.1093/oso/9780198787075.003.0019 ◽

2017 ◽

Author(s):

T. Kimura

Keyword(s):

Angular Momentum ◽

Giant Magnetoresistance ◽

Spontaneous Magnetization ◽

Magnetic Domain ◽

Magnetic Multilayers ◽

Transfer Effect ◽

Spin Transfer Torque ◽

Spin Transfer ◽

Spin Angular Momentum ◽

Spin Torques

This chapter discusses the spin-transfer effect, which is described as the transfer of the spin angular momentum between the conduction electrons and the magnetization of the ferromagnet that occurs due to the conservation of the spin angular momentum. L. Berger, who introduced the concept in 1984, considered the exchange interaction between the conduction electron and the localized magnetic moment, and predicted that a magnetic domain wall can be moved by flowing the spin current. The spin-transfer effect was brought into the limelight by the progress in microfabrication techniques and the discovery of the giant magnetoresistance effect in magnetic multilayers. Berger, at the same time, separately studied the spin-transfer torque in a system similar to Slonczewski’s magnetic multilayered system and predicted spontaneous magnetization precession.

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