scholarly journals Four-body (an)harmonic oscillator in d-dimensional space: S-states, (quasi)-exact-solvability, hidden algebra sl(7)

2021 ◽  
Vol 62 (7) ◽  
pp. 072103
Author(s):  
Adrian M. Escobar-Ruiz ◽  
Alexander V. Turbiner ◽  
Willard Miller
Keyword(s):  
Harmonic Oscillator ◽  
Dimensional Space ◽  
Exact Solvability ◽  
S States

scholarly journals Four-body problem in d-dimensional space: Ground state, (quasi)-exact-solvability. IV

2019 ◽  
Vol 60 (6) ◽  
pp. 062101 ◽  
Author(s):  
M. A. Escobar-Ruiz ◽  
Willard Miller ◽  
Alexander V. Turbiner
Keyword(s):  
Ground State ◽  
Body Problem ◽  
Dimensional Space ◽  
Exact Solvability ◽  
Four Body Problem

scholarly journals FADDEEV-JACKIW FORMALISM FOR A TOPOLOGICAL-LIKE OSCILLATOR IN PLANAR DIMENSIONS

1996 ◽  
Vol 11 (01) ◽  
pp. 69-79 ◽  
Author(s):  
C.P. NATIVIDADE ◽  
H. BOSCHI-FILHO
Keyword(s):  
Harmonic Oscillator ◽  
Dimensional Space ◽  
Constrained Systems ◽  
Electromagnetic Potential ◽  
Two Dimensional ◽  
Chern Simons

The problem of a harmonic oscillator coupling to an electromagnetic potential plus a topological-like (Chern-Simons) massive term, in two-dimensional space, is studied in the light of the symplectic formalism proposed by Faddeev and Jackiw for constrained systems.

scholarly journals PDM Damped-Driven Oscillators: Exact Solvability, Classical States Crossings, and Self-Crossings

2021 ◽  
Author(s):  
Omar Mustafa
Keyword(s):  
Harmonic Oscillator ◽  
Force Field ◽  
Dissipative Force ◽  
Classical Particle ◽  
Point Canonical Transformation ◽  
Exact Solvability ◽  
Classical State ◽  
Dependent Mass ◽  
Position Dependent Mass ◽  
Classical States

Abstract Within the standard Lagrangian and Hamiltonian setting, we consider a position-dependent mass (PDM) classical particle performing a damped driven oscillatory (DDO) motion under the influence of a conservative harmonic oscillator force field $V\left( x\right) =\frac{1}{2}\omega ^{2}Q\left( x\right) x^{2}$ and subjected to a Rayleigh dissipative force field $\mathcal{R}\left( x,\dot{x}\right) =\frac{1}{2}b\,m\left( x\right) \dot{x}^{2}$ in the presence of an external periodic (non-autonomous) force $F\left( t\right) =F_{\circ }\,\cos \left( \Omega t\right) $. Where, the correlation between the coordinate deformation $\sqrt{Q(x)}$ and the velocity deformation $\sqrt{m(x)}$ is governed by a point canonical transformation $q\left( x\right) =\int \sqrt{m\left( x\right) }dx=\sqrt{%Q\left( x\right) }x$. Two illustrative examples are used: a non-singular PDM-DDO, and a power-law PDM-DDO models. Classical-states $\{x(t),p(t)\}$ crossings are analysed and reported. Yet, we observed/reported that as a classical state $\{x_{i}(t),p_{i}(t)\}$ evolves in time it may cross itself at an earlier and/or a later time/s.

scholarly journals Three-body problem in d-dimensional space: Ground state, (quasi)-exact-solvability

2018 ◽  
Vol 59 (2) ◽  
pp. 022108 ◽  
Author(s):  
Alexander V. Turbiner ◽  
Willard Miller ◽  
M. A. Escobar-Ruiz
Keyword(s):  
Ground State ◽  
Body Problem ◽  
Dimensional Space ◽  
Three Body Problem ◽  
Exact Solvability ◽  
Three Body

scholarly journals QUANTUM EQUIVALENT OF THE BERTRAND'S THEOREM

2000 ◽  
Vol 15 (30) ◽  
pp. 1851-1857 ◽  
Author(s):  
N. GURAPPA ◽  
PRASANTA K. PANIGRAHI ◽  
T. SOLOMAN RAJU ◽  
V. SRINIVASAN
Keyword(s):  
Harmonic Oscillator ◽  
Infinite Number ◽  
Classical Result ◽  
Eigenvalue Problems ◽  
Classical Mechanics ◽  
Bound State ◽  
Central Potential ◽  
Exact Solvability ◽  
Special Cases ◽  
General Bound

A procedure for constructing general bound state potentials is given. Analogous to the Bertrand's theorem in classical mechanics, we then identify radial eigenvalue problems possessing exact solvability and infinite number of eigenstates. Akin to the classical result, the only special cases of the general central potential, satisfying the above two conditions, are the Coulomb and harmonic oscillator potentials.

scholarly journals Nonrelativistic Atomic Spectrum for Companied Harmonic Oscillator Potential and its Inverse in both NC-2D: RSP

2015 ◽  
Vol 56 ◽  
pp. 1-9 ◽  
Author(s):  
Abdelmadjid Maireche
Keyword(s):  
Harmonic Oscillator ◽  
Real Space ◽  
Gauge Condition ◽  
Oscillator Potential ◽  
Harmonic Oscillator Potential ◽  
Quadratic Potential ◽  
Shift Method ◽  
Exact Solvability ◽  
Isotropic Harmonic Oscillator ◽  
Standard Perturbation Theory

A novel study for the exact solvability of nonrelativistic quantum spectrum systems for companied Harmonic oscillator potential and its inverse (the isotropic harmonic oscillator plus inverse quadratic potential) is discussed used both Boopp’s shift method and standard perturbation theory in both noncommutativity two dimensional real space and phase (NC-2D: RSP), furthermore the exact corrections for the spectrum of studied potential was depended on two infinitesimals parameters θ and θ¯ which plays an opposite rolls, this permits us to introduce a new fixing gauge condition and we have also found the corresponding noncommutative anisotropic Hamiltonian.

HARMONIC OSCILLATOR IN NONCOMMUTING TWO-DIMENSIONAL SPACE

2007 ◽  
Vol 21 (32) ◽  
pp. 5363-5380
Author(s):  
ANTONY STREKLAS
Keyword(s):  
Magnetic Field ◽  
Partition Function ◽  
Thermodynamic Properties ◽  
Harmonic Oscillator ◽  
Deformation Parameter ◽  
Dimensional Space ◽  
Dimensional System ◽  
Two Dimensional ◽  
Two Dimensional System ◽  
The Magnetic Field

In the present paper, we study a two-dimensional harmonic oscillator in a constant magnetic field in noncommuting space. We use the following Hamiltonian [Formula: see text] with commutation relations [Formula: see text] and [Formula: see text]. The parameter λ expresses the presence of the magnetic field. We find the exact propagator of the system and the time evolution of the basic operators. We prove that the system is equivalent to a two-dimensional system where the operators of momentum and coordinates of the second dimension satisfy a deformed commutation relation [Formula: see text]. The deformation parameter, μ, depends on λ and θ, and is independent of the Hamiltonian. Finally, we investigate the thermodynamic properties of the system in Boltzmann statistics. We find the statistical density matrix and the partition function, which is equivalent to that of a two-dimensional harmonic oscillator with two deformed frequencies Ω1 and Ω2.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

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