Properties Of Shift Operators Research Articles

On the nonlinear Fock description of quantum systems with quadratic spectra

The nonlinear version of the Fock approach, developed previously for systems with (extended) equidistant spectra (Eleonsky V M and Korolev V G 1995 J. Phys. A: Math. Gen. 28 4973), is also shown to describe systems with quadratic spectra. Some general properties of shift operators for such spectra are studied. It is found, in particular, that families of shift operators related to the generators of the algebra su(1,1) as well as supersymmetry ladder operators arise naturally in that approach in a unified way.

Shift operator techniques for the classification of multipole-phonon states: IV. Properties of shift operators in the G2 group

A previously developed shift operator method is applied to the G2 group, which plays an important role in the classification of nuclear octupole-phonon states. Expressions which connect quadratic products of the considered shift operators with G2 invariants are derived.

Shift operator techniques for the classification of multipole-phonon states. V. Properties of shift operators in the R(7) group

With a view to obtaining additional label-generating operators for the classification of octupole-phonon states a set of shift operators Okl (k=0, ±1, ±2, ±3) in the R(7) group is constructed. Expressions which connect quadratic products of these shift operators are given, and it turns out that besides R(7) invariants the expressions also involve the scalar G2 shift operator P0l previously studied. The opportunity to arrive at an orthogonal solution of the state labelling problem is discussed.

Shift-operator techniques for the classification of multipole-phonon states. I. Properties of shift operators in the R(5) group

With a view to obtaining an orthogonal solution to the state labeling problem of the nuclear quadrupole-phonon states, independent operators which shift the eigenvalues of the R(3) Casimir operator L2 are constructed. Expressions which connect quadratic products of these shift operators with R(5) invariants are given.