Time-dependent raising and lowering operators for the ageing, forced and damped oscillator in quantum mechanics

Within the standard quantum mechanics a q-deformation of the simplest N=2 supersymmetry algebra is suggested. Resulting physical systems do not have conserved charges and degeneracies in the spectra. Instead, superpartner Hamiltonians are q-isospectral, i.e., the spectrum of one can be obtained from another (with possible exception of the lowest level) by the q2-factor scaling. A special class of the self-similar potentials is shown to obey the dynamical conformal symmetry algebra su q(1,1). These potentials exhibit exponential spectra and corresponding raising and lowering operators satisfy the q-deformed harmonic oscillator algebra of Biedenharn and Macfarlane.

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SUPERCONFORMAL QUANTUM MECHANICS VIA WIGNER–HEISENBERG ALGEBRA

Modern Physics Letters A ◽

10.1142/s0217732310033475 ◽

2010 ◽

Vol 25 (29) ◽

pp. 2507-2521 ◽

Cited By ~ 2

Author(s):

H. L. CARRION ◽

R. DE LIMA RODRIGUES

Keyword(s):

Quantum Mechanics ◽

Energy Spectrum ◽

Casimir Operator ◽

Conformal Symmetry ◽

Heisenberg Algebra ◽

Raising And Lowering Operators ◽

Parity Operator ◽

Conformal Quantum Mechanics ◽

Lowering Operators ◽

Natural Relation

We show the natural relation between the Wigner Hamiltonian and the conformal Hamiltonian. A model in (super)conformal quantum mechanics with (super)conformal symmetry in the Wigner–Heisenberg algebra picture [x, px] = i(1+cP) (P being the parity operator) is presented. In this context, the energy spectrum, the Casimir operator, raising and lowering operators are defined.

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Construction and Characterization of Representations of SU(7) for GUT Model Builders

Symmetry ◽

10.3390/sym13061044 ◽

2021 ◽

Vol 13 (6) ◽

pp. 1044

Author(s):

Daniel Jones ◽

Jeffery A. Secrest

Keyword(s):

Gauge Symmetry ◽

Symmetry Group ◽

Lie Group ◽

Cartan Subalgebra ◽

Natural Extension ◽

Grand Unification ◽

Raising And Lowering Operators ◽

Higher Dimensional ◽

Lowering Operators

The natural extension to the SU(5) Georgi-Glashow grand unification model is to enlarge the gauge symmetry group. In this work, the SU(7) symmetry group is examined. The Cartan subalgebra is determined along with their commutation relations. The associated roots and weights of the SU(7) algebra are derived and discussed. The raising and lowering operators are explicitly constructed and presented. Higher dimensional representations are developed by graphical as well as tensorial methods. Applications of the SU(7) Lie group to supersymmetric grand unification as well as applications are discussed.

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HAPPER'S CURIOUS DEGENERACIES AND YANGIAN

International Journal of Modern Physics B ◽

10.1142/s0217979202011573 ◽

2002 ◽

Vol 16 (14n15) ◽

pp. 1867-1873 ◽

Cited By ~ 3

Author(s):

CHENG-MING BAI ◽

MO-LIN GE ◽

KANG XUE

Keyword(s):

Representation Theory ◽

Algebraic Structure ◽

Zeeman Effect ◽

Tensor Space ◽

Commutation Relations ◽

Raising And Lowering Operators ◽

Degenerate States ◽

Lowering Operators

We find raising and lowering operators distinguishing the degenerate states for the Hamiltonian [Formula: see text] at x = ± 1 for spin 1 that was given by Happer et al.1,2 to interpret the curious degeneracies of the Zeeman effect for condensed vapor of 87 Rb . The operators obey Yangian commutation relations. We show that the curious degeneracies seem to verify the Yangian algebraic structure for quantum tensor space and are consistent with the representation theory of Y(sl(2)).

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