Generalization of the Runge-Lenz Vector in the Presence of an Electric Field

Redmond, P. J.

doi:10.1103/physrev.133.b1352

Cited by 51 publications

(26 citation statements)

References 3 publications

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“…The Runge-Lenz type scalar K z is proportional to the projection of the Runge-Lenz vector on the electric field, augmented with a correction term [19], 3. General polynomial solutions to (2.14) are obtained [20] for any integer n = 0, ±1, .…”

Section: Further Separable Perturbationsmentioning

confidence: 99%

Separability and dynamical symmetry of Quantum Dots

et al. 2014

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The separability and Runge-Lenz-type dynamical symmetry of the internal dynamics of certain two-electron Quantum Dots, found by Simonović et al. [1], is traced back to that of the perturbed Kepler problem. A large class of axially symmetric perturbing potentials which allow for separation in parabolic coordinates can easily be found. Apart of the 2:1 anisotropic harmonic trapping potential considered in [1], they include a constant electric field parallel to the magnetic field (Stark effect), the ring-shaped Hartmann potential, etc. The harmonic case is studied in detail.

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Section: Further Separable Perturbationsmentioning

confidence: 99%

Separability and dynamical symmetry of Quantum Dots

et al. 2014

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“…Fortunately, for the reasons mentioned earlier, the dynamics of the orbit with the asymmetric wind are remarkably similar to the Kepler problem. Redmond (1964) found a generalization of the Runge–Lenz vector in the presence of an external force ( F = F 1 ). Specifically, the generalized Runge–Lenz vector is given by where M is the total mass of the binary, μ is the reduced mass of the binary, L is the orbital angular momentum, r is the relative position of the two stars and p is their relative momentum.…”

Section: Calculationsmentioning

confidence: 99%

Orbital evolution with white-dwarf kicks

Heyl

2007

Monthly Notices of the Royal Astronomical Society

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Recent observations of white dwarfs in globular clusters indicate that these stars may get a velocity kick during their time as giants. This velocity kick could originate naturally if the mass loss while on the asymptotic giant branch is slightly asymmetric. If white dwarfs get a kick comparable to the orbital velocity of the binary, the initial Runge-Lenz vector (eccentricity vector) of the orbit is damped to be replaced by a component pointing toward the cross product of the initial angular momentum and the force. The final eccentricity may be of order unity and if the kick is sufficiently large, the system may be disrupted. These results may have important ramifications for the evolution of binary stars and planetary systemsComment: 6 pages, 2 figures, added many intermediate equations, version accepted by MNRA

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“…The quantum pendulum [123] is described by the replacement rn + Z (I-moment of inertia), Z e 2 + Zg, (g-gravitational acceleration) and E = b = 0.…”

Section: )mentioning

confidence: 99%

Coulomb Potentials by Path Integration

Grosche

1992

Fortschr. Phys.

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The path integral for the potential is evaluated in three different coordinate systems, i. e. in cartesian coordinates, in polar coordinates and in parabolic coordinates. The equivalence between the different approaches is shown and in each case the energyspectrum and the wave functions are explicitly calculated. Furthermore we discuss special cases, including the ring‐potential, the Coulomb potential with an Aharonov‐Bohm solenoid, and the genuine Coulomb problem. We also point out the separability of the path integral formulation of the ring‐potential in spheroidal coordinates, and of the Coulomb potential in spheroidal and spheroconical coordinates, respectively.

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Generalization of the Runge-Lenz Vector in the Presence of an Electric Field

Cited by 51 publications

References 3 publications

Separability and dynamical symmetry of Quantum Dots

Separability and dynamical symmetry of Quantum Dots

Orbital evolution with white-dwarf kicks

Coulomb Potentials by Path Integration

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