New Hamiltonians with closed orbits

Jamil Daboul; Mark Hickman

doi:10.1016/S0375-9601(00)00105-5

New Hamiltonians with closed orbits

Jamil Daboul, Mark Hickman

Department of Physics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

By considering energy-dependent coupling constants, we arrive at a class of ‘pseudo-free Hamiltonians’ of the form H = p²/2m(r), where the effective mass depends on the radius r. We prove that these Hamiltonians can reproduce the E ≠ 0 and L ≠ 0 orbits r = r(φ) of standard Hamiltonians with central potentials. In particular, two cases yield closed elliptical orbits but violate Kepler’s law of areas. Other peculiarities and generalizations are discussed.

Original language	English
Pages (from-to)	232-239
Number of pages	8
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	267
Issue number	4
DOIs	https://doi.org/10.1016/S0375-9601(00)00105-5
State	Published - 20 Mar 2000

Keywords

Boundary conditions
Closed orbits
Conservation laws
Energy-dependent potentials
Integrable models
Kepler law of areas
Runge-Lenz vector
Variable mass

ASJC Scopus subject areas

Physics and Astronomy (all)

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10.1016/S0375-9601(00)00105-5

Cite this

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title = "New Hamiltonians with closed orbits",

abstract = "By considering energy-dependent coupling constants, we arrive at a class of {\textquoteleft}pseudo-free Hamiltonians{\textquoteright} of the form H = p2/2m(r), where the effective mass depends on the radius r. We prove that these Hamiltonians can reproduce the E ≠ 0 and L ≠ 0 orbits r = r(φ) of standard Hamiltonians with central potentials. In particular, two cases yield closed elliptical orbits but violate Kepler{\textquoteright}s law of areas. Other peculiarities and generalizations are discussed.",

keywords = "Boundary conditions, Closed orbits, Conservation laws, Energy-dependent potentials, Integrable models, Kepler law of areas, Runge-Lenz vector, Variable mass",

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TY - JOUR

T1 - New Hamiltonians with closed orbits

AU - Daboul, Jamil

AU - Hickman, Mark

PY - 2000/3/20

Y1 - 2000/3/20

N2 - By considering energy-dependent coupling constants, we arrive at a class of ‘pseudo-free Hamiltonians’ of the form H = p2/2m(r), where the effective mass depends on the radius r. We prove that these Hamiltonians can reproduce the E ≠ 0 and L ≠ 0 orbits r = r(φ) of standard Hamiltonians with central potentials. In particular, two cases yield closed elliptical orbits but violate Kepler’s law of areas. Other peculiarities and generalizations are discussed.

AB - By considering energy-dependent coupling constants, we arrive at a class of ‘pseudo-free Hamiltonians’ of the form H = p2/2m(r), where the effective mass depends on the radius r. We prove that these Hamiltonians can reproduce the E ≠ 0 and L ≠ 0 orbits r = r(φ) of standard Hamiltonians with central potentials. In particular, two cases yield closed elliptical orbits but violate Kepler’s law of areas. Other peculiarities and generalizations are discussed.

KW - Boundary conditions

KW - Closed orbits

KW - Conservation laws

KW - Energy-dependent potentials

KW - Integrable models

KW - Kepler law of areas

KW - Runge-Lenz vector

KW - Variable mass

UR - http://www.scopus.com/inward/record.url?scp=0005290221&partnerID=8YFLogxK

U2 - 10.1016/S0375-9601(00)00105-5

DO - 10.1016/S0375-9601(00)00105-5

M3 - Article

AN - SCOPUS:0005290221

SN - 0375-9601

VL - 267

SP - 232

EP - 239

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 4

ER -

New Hamiltonians with closed orbits

Abstract

Keywords

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