Dynamical symmetry group of the relativistic Coulomb problem in the quasipotential approach

1989 ◽  
Vol 80 (1) ◽  
pp. 697-702 ◽  
Author(s):  
Sh. M. Nagiev
Keyword(s):  
Symmetry Group ◽  
Dynamical Symmetry ◽  
Quasipotential Approach ◽  
Coulomb Problem ◽  
Relativistic Coulomb

Relativistic Coulomb problem in curved spaces

2019 ◽  
Vol 127 (1) ◽  
pp. 10005 ◽  
Author(s):  
Dai-Nam Le ◽  
Anh-Luan Phan ◽  
Van-Hoang Le ◽  
Pinaki Roy
Keyword(s):  
Coulomb Problem ◽  
Curved Spaces ◽  
Relativistic Coulomb

PARASUPERSYMMETRIC COHERENT STATES FOR LANDAU LEVELS WITH DYNAMICAL SYMMETRY GROUP H4

2002 ◽  
Vol 17 (28) ◽  
pp. 4081-4093 ◽  
Author(s):  
H. FAKHRI ◽  
H. MOTAVALI
Keyword(s):  
Magnetic Field ◽  
Symmetry Group ◽  
Coherent States ◽  
Ad Hoc ◽  
Flat Surface ◽  
Arbitrary Order ◽  
Dynamical Symmetry ◽  
Quantum States ◽  
Landau Levels ◽  
Lowering Operator

The eigenstates and their degeneracy for parasupersymmetric Hamiltonian of arbitrary order p, corresponding to the motion of a charged particle with spin [Formula: see text] on the flat surface in the presence of a constant magnetic field along z-axis, are calculated. The eigenstates are expressed in terms of Landau levels quantum states with dynamical symmetry group H4. Furthermore, parasupersymmetric coherent states with multiplicity degeneracy are derived for an ad hoc lowering operator of the eigenstates in terms of ordinary coherent states of Landau Hamiltonian.

scholarly journals Dynamical Symmetries of the 2D Newtonian Free Fall Problem Revisited

Symmetry ◽  
2021 ◽  
Vol 14 (1) ◽  
pp. 27
Author(s):  
Tuong Trong Truong
Keyword(s):  
Symmetry Group ◽  
Anharmonic Oscillator ◽  
Symmetry Algebra ◽  
Functional Space ◽  
Free Fall ◽  
Dynamical Symmetry ◽  
Functional Integral ◽  
Theoretical Physics ◽  
Classical Level ◽  
Dynamical Symmetries

Among the few exactly solvable problems in theoretical physics, the 2D (two-dimensional) Newtonian free fall problem in Euclidean space is perhaps the least known as compared to the harmonic oscillator or the Kepler–Coulomb problems. The aim of this article is to revisit this problem at the classical level as well as the quantum level, with a focus on its dynamical symmetries. We show how these dynamical symmetries arise as a special limit of the dynamical symmetries of the Kepler–Coulomb problem, and how a connection to the quartic anharmonic oscillator problem, a long-standing unsolved problem in quantum mechanics, can be established. To this end, we construct the Hilbert space of states with free boundary conditions as a space of square integrable functions that have a special functional integral representation. In this functional space, the free fall dynamical symmetry algebra is shown to be isomorphic to the so-called Klink’s algebra of the quantum quartic anharmonic oscillator problem. Furthermore, this connection entails a remarkable integral identity for the quantum quartic anharmonic oscillator eigenfunctions, which implies that these eigenfunctions are in fact zonal functions of an underlying symmetry group representation. Thus, an appropriate representation theory for the 2D Newtonian free fall quantum symmetry group may potentially open the way to exactly solving the difficult quantization problem of the quartic anharmonic oscillator. Finally, the initial value problem of the acoustic Klein–Gordon equation for wave propagation in a sound duct with a varying circular section is solved as an illustration of the techniques developed here.

REPRESENTATION OF THE HEISENBERG ALGEBRA h4 BY THE LOWEST LANDAU LEVELS AND THEIR COHERENT STATES

2005 ◽  
Vol 20 (30) ◽  
pp. 2295-2303
Author(s):  
H. FAKHRI ◽  
Z. SHADMAN
Keyword(s):  
Symmetry Group ◽  
Lie Algebra ◽  
Coherent States ◽  
Rotational Symmetry ◽  
Dynamical Symmetry ◽  
Heisenberg Algebra ◽  
Landau Levels ◽  
Shape Invariance ◽  
Half Axis

Using simultaneous shape invariance with respect to two different parameters, we introduce a pair of appropriate operators which realize shape invariance symmetry for the monomials on a half-axis. It leads to the derivation of rotational symmetry and dynamical symmetry group H4 with infinite-fold degeneracy for the lowest Landau levels. This allows us to represent the Heisenberg–Lie algebra h4 not only by the lowest Landau levels, but also by their corresponding standard coherent states.

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