Algebraic treatment of the Stark effect for hydrogen

Lopes, Amauri; Ferreira, P. Leal

doi:10.1007/bf02899938

Cited by 4 publications

(2 citation statements)

References 7 publications

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“…Calculation of the perturbation expansion for the energy shift, which is known to be asymptotic, is discussed in Schrodinger [49], Mendelsohn [50], Silverstone [5 11, (obtaining the expansion to all orders); by Alliluev and Malkin [52], and by Lopes and Ferreira [53] using the dynamical (Runge-Lenz) symmetries of the hydrogen atom to obtain explicit algebraic expressions; and by Herbst and Simon [54] who estimated the asymptotic form of the coefficients and proved Bore1 summability of the series.…”

Section: Appendixmentioning

confidence: 99%

Complex coordinates and the Stark effect

Cerjan

Hedges

Holt

et al. 1978

Int J of Quantum Chemistry

106

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The theories of the dilatation, r + r eie, and translation, x --t x + iq, transformations as related to the Stark problem are reviewed, and new results obtained. Results for the hydrogen atom n = 1 and n = 2 levels and the 'Po, 2s2p H-shape resonance in dc fields are presented, and the extension to the ac Stark effect made. Spectral estimates are made using the technique of the numerical range and via discussion of several model problems, using both coordinate rotation and coordinate translation.

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Section: Appendixmentioning

confidence: 99%

Complex coordinates and the Stark effect

Cerjan

Hedges

Holt

et al. 1978

Int J of Quantum Chemistry

106

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“…The SO(2, 1) group, or alternatively, the SU(1, 1) group deals with the radial contributions that shift the principal quantum numbers [50][51][52]. Even though the SO(4, 2) group allows the dipole matrix elements to be calculated, the use of the dynamical group tends to perturbation treatments [53,54]. In contrast, our algebraic approach is not based on the use of the dynamical group, instead, our approach falls in the framework of a discrete variable representation approach, whose salient feature consists in its simplicity as we next present.…”

Section: Stark Effectmentioning

confidence: 99%

Algebraic DVR Approaches Applied to Describe the Stark Effect

et al. 2020

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Two algebraic approaches based on a discrete variable representation are introduced and applied to describe the Stark effect in the non-relativistic Hydrogen atom. One approach consists of considering an algebraic representation of a cutoff 3D harmonic oscillator where the matrix representation of the operators r2 and p2 are diagonalized to define useful bases to obtain the matrix representation of the Hamiltonian in a simple form in terms of diagonal matrices. The second approach is based on the U(4) dynamical algebra which consists of the addition of a scalar boson to the 3D harmonic oscillator space keeping constant the total number of bosons. This allows the kets associated with the different subgroup chains to be linked to energy, coordinate and momentum representations, whose involved branching rules define the discrete variable representation. Both methods, although originating from the harmonic oscillator basis, provide different convergence tests due to the fact that the associated discrete bases turn out to be different. These approaches provide powerful tools to obtain the matrix representation of 3D general Hamiltonians in a simple form. In particular, the Hydrogen atom interacting with a static electric field is described. To accomplish this task, the diagonalization of the exact matrix representation of the Hamiltonian is carried out. Particular attention is paid to the subspaces associated with the quantum numbers n=2,3 with m=0.

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Calculation of high-order electric polarizabilities via the perturbational-variational Rayleigh-Ritz formalism: Application to the hydrogenic Stark effect

Silverman

Hinze

1988

Phys. Rev. A

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Algebraic treatment of the Stark effect for hydrogen

Cited by 4 publications

References 7 publications

Complex coordinates and the Stark effect

Complex coordinates and the Stark effect

Algebraic DVR Approaches Applied to Describe the Stark Effect

Calculation of high-order electric polarizabilities via the perturbational-variational Rayleigh-Ritz formalism: Application to the hydrogenic Stark effect

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