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Piña, E.; Jiménez-Lara, Lidia

doi:10.1023/a:1013865801564

Cited by 5 publications

(3 citation statements)

References 2 publications

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“…On the other hand the more recent work [4] deals with the use of the hyperspherical elliptic coordinates and harmonic basis sets in the fifth dimensional sphere S 5 for the study of the three-body problem in quantum mechanics. Its classical astronomical counterpart [28] uses the relative radial coordinate of the first two particles and the radial coordinate of the third particle relative to the center of mass of the first two, instead of the hyper-radius and one of the five angular coordinates in S 5 . It is also pertinent to mention Sasaki's contribution in the Symposium, "Exactly solvable quantum mechanics and infinite families of multi-indexed orthogonal polynomials", and to cite [22,23], involving Hamiltonians with tridiagonal matrix representations.…”

Section: Discussionmentioning

confidence: 99%

Ladder Operators for Lamé Spheroconal Harmonic Polynomials

Méndez-Fragoso

Ley‐Koo

2012

SIGMA

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Abstract. Three sets of ladder operators in spheroconal coordinates and their respective actions on Lamé spheroconal harmonic polynomials are presented in this article. The polynomials are common eigenfunctions of the square of the angular momentum operator and of the asymmetry distribution Hamiltonian for the rotations of asymmetric molecules, in the body-fixed frame with principal axes. The first set of operators for Lamé polynomials of a given species and a fixed value of the square of the angular momentum raise and lower and lower and raise in complementary ways the quantum numbers n 1 and n 2 counting the respective nodal elliptical cones. The second set of operators consisting of the cartesian componentsL x ,L y ,L z of the angular momentum connect pairs of the four species of polynomials of a chosen kind and angular momentum. The third set of operators, the cartesian componentsp x ,p y ,p z of the linear momentum, connect pairs of the polynomials differing in one unit in their angular momentum and in their parities. Relationships among spheroconal harmonics at the levels of the three sets of operators are illustrated.

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Section: Discussionmentioning

confidence: 99%

Ladder Operators for Lamé Spheroconal Harmonic Polynomials

Méndez-Fragoso

Ley‐Koo

2012

SIGMA

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“…4 to the Cartesian inertial frame. First, we put the origin of coordinates at the center of mass of the three particles, and we choose the third coordinate of each particle to be zero.…”

Section: Appendixmentioning

confidence: 99%

“…3 in the way of Ref. 4 to show that for a potential k/r 2 there is an extra constant of motion that allows us to separate the motion of the total inertia moment. We then introduce appropriate dimensionless variables in order to reduce the number of parameters, and we give a global description of the total inertia moment variable.…”

Section: Introductionmentioning

confidence: 96%

The three-body problem with an inverse square law potential

Jiménez-Lara

Piña

2003

Journal of Mathematical Physics

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The super-separability of the three-body inverse-square Calogero systemWe study the motion of three masses in a plane interacting with a central potential proportional to 1/r 2 using the coordinates introduced recently by Piña. We show that this problem with four degrees of freedom ͑three angles and a distance related to the inertia moment of the system in these coordinates͒ is partially separable, and can be reduced to a problem with two degrees of freedom ͑two angles͒ with a new constant of motion. We find a symmetry of reflection ͑an involution͒ for this system and we use the symmetry lines to find periodic orbits in the angular coordinates. These orbits will not be periodic in general on the whole phase space because the coordinate of distance type grows as t when t→ϱ and it is unbounded. However, if the inertia moment of the system remains constant, they will be periodic on the whole phase space.

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Perturbing the Lagrange Solution to the General Three Body Problem

Piña

Jiménez-Lara

2004

New Advances in Celestial Mechanics and Hamiltonian Systems

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Cited by 5 publications

References 2 publications

Ladder Operators for Lamé Spheroconal Harmonic Polynomials

Ladder Operators for Lamé Spheroconal Harmonic Polynomials

The three-body problem with an inverse square law potential

Perturbing the Lagrange Solution to the General Three Body Problem

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