aqora

Matrix Representation about Spin Angular Momentum Operator and Eigenvector on System of Double Electrons

Jianwei Wang

Express in self representation about spin angular momentum Operator,eigenvector on system of double electrons and transformation each other about ^S_z,^S_x,^S_y representation have been discussed with the theory of representation.We have got succinct practical express form.

Journal of Kashgar Teachers CollegeJan 1, 20060 citations

Rotation-operator approach and spin dynamics in a time-varying magnetic field

Jinyuan Zhou, Chaohui Ye

The evolution operator for an arbitrary spin system in an arbitrary time-varying magnetic field is disentangled into the rotation operator; consequently, the time-ordering problem is shifted into solving the Euler geometric equations. Some realistic transformations are proposed in order to find their analytic solutions. The probabilities and phases characterizing state transitions are also analyzed.

Physical Review AAug 1, 199410 citations

Eigenvalues of S⋅Π for spins 1/2, 1, and 3/2

David Leo Weaver

The eigenvalues of the matrix operator S⋅Π for a constant magnetic field are derived in a parallel way for spins 1/2, 1, and 3/2 using only the algebra of the spin matrices and the commutation relations of the components of Π.

Journal of Mathematical PhysicsJan 1, 19787 citations

Spin realization of Y(SL(2)) algebra in magnetic field and eigenvectors

Chunjie Li

According to the theory of Yangian algebra,this paper gives spin realization of Y(SL(2)) algebra of two spin-1/2 coupling system in an extra time magnetic field.By constructing transform operator,eigenvectors of this spin coupling system are also given.

Journal of Changchun UniversityJan 1, 20070 citations

Photon position operators and localized bases

Margaret Hawton, W. E. Baylis

We extend a procedure for the construction of photon position operators with transverse eigenvectors and commuting components [Phys. Rev. A 59, 954 (1999)] to body rotations described by three Euler angles. The axial angle can be made a function of the two polar angles, and different choices of the functional dependence are analogous to different gauges of a magnetic field. Symmetries broken by a choice of gauge are reestablished by transformations within the gauge group. The approach allows several previous proposals to be related. Because of the coupling of the photon momentum and spin, our position operator, like that proposed by Pryce, is a matrix that does not commute with the spin operator. Unlike the Pryce operator, however, our operator has commuting components, but the commutators of these components with the total angular momentum require an extra term to rotate the matrices for each vector component around the momentum direction. Several proofs of the nonexistence of a photon position operator with commuting components are based on overly restrictive premises that do not apply here.We extend a procedure for the construction of photon position operators with transverse eigenvectors and commuting components [Phys. Rev. A 59, 954 (1999)] to body rotations described by three Euler angles. The axial angle can be made a function of the two polar angles, and different choices of the functional dependence are analogous to different gauges of a magnetic field. Symmetries broken by a choice of gauge are reestablished by transformations within the gauge group. The approach allows several previous proposals to be related. Because of the coupling of the photon momentum and spin, our position operator, like that proposed by Pryce, is a matrix that does not commute with the spin operator. Unlike the Pryce operator, however, our operator has commuting components, but the commutators of these components with the total angular momentum require an extra term to rotate the matrices for each vector component around the momentum direction. Several proofs of the nonexistence of a photon position operator with commuting components are based on overly restrictive premises that do not apply here.

arXiv:quant-ph/0101011Physical Review AJun 5, 200150 citations

Eigen value and eigen function for electron in magnetic field using relativistic quantum mechanics

Abbas Ahmed Ali

Maǧallaẗ ǧāmiʻaẗ Karbalāʼ/Maǧallaẗ ǧāmiʻaẗ karbalāʼJan 1, 20100 citations

Eigenvectors of Spin System in an Extra Time Magnetic Field

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Eigenvectors of Spin System in an Extra Time Magnetic Field

Abstract

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