Orbital angular momentum eigenfunctions for many-particle systems

1985 ◽  
Vol 63 (7) ◽  
pp. 1719-1722 ◽  
Author(s):  
John Avery
Keyword(s):  
Angular Momentum ◽  
Symmetric Group ◽  
Orbital Angular Momentum ◽  
Particle System ◽  
Total Spin ◽  
Particle Systems ◽  
Irreducible Representations ◽  
Angular Momentum Operator ◽  
Total Orbital Angular Momentum ◽  
Orbital Angular Momentum Operator

Methods are presented for constructing eigenfunctions of the total orbital angular momentum operator of a many-particle system without the use of the Clebsch–Gordan coefficients. One of the equations derived in this paper is analogous to Dirac's identity for total spin; and through this equation, a connection is established between eigenfunctions of L2 and irreducible representations of the symmetric group Sn.

Basis states for equivalent electrons. II. States for the Lie group Sp(4l + 2)

1980 ◽  
Vol 58 (12) ◽  
pp. 1724-1728
Author(s):  
William R. Ross
Keyword(s):  
Angular Momentum ◽  
Irreducible Representation ◽  
Orbital Angular Momentum ◽  
Lie Group ◽  
Total Spin ◽  
Irreducible Representations ◽  
Total Orbital Angular Momentum ◽  
Intermediate Group ◽  
Slater Basis

The Slater basis states for N equivalent electrons form the basis for the irreducible representation (1N) of the Lie group U(4l + 2). States which are eigenfunctions of the total spin and total orbital angular momentum form the basis for irreducible representations of SO(3) × SU(2). In this paper the intermediate group Sp(4l + 2) is studied. The basis states for irreducible representations of Sp(4l + 2) are expressed in terms of the Slater basis states.

scholarly journals GLUEBALL SPIN

2001 ◽  
Vol 16 (01) ◽  
pp. 41-51
Author(s):  
D. SINGLETON
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Momentum Operator ◽  
Angular Momentum Operator ◽  
Total Field ◽  
Expectation Value ◽  
Starting Point ◽  
Simplifying Assumptions

The spin of a glueball is usually taken as coming from the spin (and possibly the orbital angular momentum) of its constituent gluons. In light of the difficulties in accounting for the spin of the proton from its constituent quarks, the spin of glueballs is re-examined. The starting point is the fundamental QCD field angular momentum operator written in terms of the chromoelectric and chromomagnetic fields. First, we look at the possible restrictions placed on the structure of glueballs from the requirement that the QCD field angular momentum operator should satisfy the standard commutation relationships. This analysis can be compared to the electromagnetic charge/monopole system, where the requirement that the total field angular momentum obey the angular momentum commutation relationships places restrictions (i.e. the Dirac condition) on the system. Second, we look at the expectation value of the field angular momentum operator under some simplifying assumptions.

scholarly journals Spherical HarmonicsYlm(θ,ϕ): Positive and Negative Integer Representations ofsu(1,1)forl-mandl+m

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
H. Fakhri
Keyword(s):  
Angular Momentum ◽  
Irreducible Representation ◽  
Lie Algebra ◽  
Spherical Harmonics ◽  
Compact Manifold ◽  
Unitary Irreducible Representation ◽  
Irreducible Representations ◽  
Angular Momentum Operator ◽  
Quantum Numbers ◽  
Azimuthal Quantum Number

The azimuthal and magnetic quantum numbers of spherical harmonicsYlm(θ,ϕ)describe quantization corresponding to the magnitude andz-component of angular momentum operator in the framework of realization ofsu(2)Lie algebra symmetry. The azimuthal quantum numberlallocates to itself an additional ladder symmetry by the operators which are written in terms ofl. Here, it is shown that simultaneous realization of both symmetries inherits the positive and negative(l-m)- and(l+m)-integer discrete irreducible representations forsu(1,1)Lie algebra via the spherical harmonics on the sphere as a compact manifold. So, in addition to realizing the unitary irreducible representation ofsu(2)compact Lie algebra via theYlm(θ,ϕ)’s for a givenl, we can also representsu(1,1)noncompact Lie algebra by spherical harmonics for given values ofl-mandl+m.

Decoupling of measured spherical tensor components of resolved J states of collisionally excited (Ar)+

1996 ◽  
Vol 74 (11-12) ◽  
pp. 955-958 ◽  
Author(s):  
O. Yenen ◽  
B. W. Moudry ◽  
D. H. Jaecks
Keyword(s):  
Angular Momentum ◽  
Density Matrix ◽  
Nonlinear Equations ◽  
Total Spin ◽  
Reflection Symmetry ◽  
Density Matrices ◽  
Total Orbital Angular Momentum ◽  
Orientation Parameters ◽  
Single Set

We measured Stoke's parameters P1, P2, P3, and P4 of excited Ar+ in coincidence with the scattered He for the two-electron process[Formula: see text]From the measured Stoke's parameters of the 4610 Å (1 Å = 10−10 m) radiation of the 2F(J = 7/2) to the 2D(J = 5/2) transition and the 4590 Å radiation of the 2F(J = 5/2) to 2D(J = 3/2) transition we determined the alignment and orientation parameters of the upper states using the Fano–Macek formalism. These parameters were then converted to the appropriate spherical tensor components in the J representation to obtain, in general eight values of [Formula: see text]. Since these states are best described by LS coupling, we decoupled the spherical tensor components of the density matrix of each J state in terms of the spherical components of the density matrices of the total orbital angular momentum L and total spin 5. The unknowns in the expansion are [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], with [Formula: see text] because of reflection symmetry. We used Mathematica to calculate the decoupling coefficients and solve these nonlinear equations. The decoupling also allows us to optically determine the octopole moments of the total orbital momentum provided that [Formula: see text] is nonzero. When [Formula: see text], the two sets of equations are linearly dependent. In this case, the determination of a single set of [Formula: see text] specifies [Formula: see text].

On the construction of irreducible representations of the symmetric group

1961 ◽  
Vol 57 (2) ◽  
pp. 330-340 ◽  
Author(s):  
J. R. Gabriel
Keyword(s):  
Symmetric Group ◽  
Quantum Mechanical Calculation ◽  
Particle Systems ◽  
Irreducible Representations ◽  
Quantum Mechanical ◽  
Simple Method ◽  
Mechanical Calculation ◽  
Digital Computers

ABSTRACTA simple method for constructing irreducible representations of the symmetric group is given. It is particularly suitable for use in quantum mechanical calculation of interactions in many particle systems, using electronic digital computers.

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