On Scattering and Bound States for a Singular Potential

We use the Tridiagonal Representation Approach (TRA) to obtain exact bound states solution (energy spectrum and wave function) of the Schrödinger equation for a three-parameter short-range potential with [Formula: see text], [Formula: see text] and [Formula: see text] singularities at the origin. The solution is a finite series of square-integrable functions with expansion coefficients that satisfy a three-term recursion relation. The solution of the recursion is a non-conventional orthogonal polynomial with discrete spectrum. The results of this work could be used to study the binding of an electron to a molecule with an effective electric quadrupole moment which has the same [Formula: see text] singularity.

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Exact bound states for the central fraction power singular potential $$V(r) = \alpha r^{2/3} + \beta r^{ - 2/3} + \gamma r^{ - 4/3} $$ .

Il Nuovo Cimento B ◽

10.1007/bf02726685 ◽

1994 ◽

Vol 109 (11) ◽

pp. 1217-1220 ◽

Cited By ~ 25

Author(s):

S. K. Bose

Keyword(s):

Bound States ◽

Singular Potential ◽

Exact Bound

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Upper Bound for the Number of Bound States Induced by the Curvature of Singular Potential

Reports on Mathematical Physics ◽

10.1016/s0034-4877(12)60006-8 ◽

2011 ◽

Vol 68 (2) ◽

pp. 225-240 ◽

Cited By ~ 5

Author(s):

Jerzy Cisło ◽

Sylwia Kondej

Keyword(s):

Upper Bound ◽

Bound States ◽

Singular Potential

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Recent Radiative and Collisional Atomic Data of Astrophysical Interest

International Astronomical Union Colloquium ◽

10.1017/s0252921100107596 ◽

1988 ◽

Vol 102 ◽

pp. 129-132

Author(s):

K.L. Baluja ◽

K. Butler ◽

J. Le Bourlot ◽

C.J. Zeippen

Keyword(s):

Mass Production ◽

Bound States ◽

Physical Models ◽

Impact Excitation ◽

Electron Impact Excitation ◽

Atomic Data ◽

Isoelectronic Sequence ◽

Astrophysical Interest ◽

Radiative Transitions ◽

Forbidden Transitions

SummaryUsing sophisticated computer programs and elaborate physical models, accurate radiative and collisional atomic data of astrophysical interest have been or are being calculated. The cases treated include radiative transitions between bound states in the 2p4and 2s2p5configurations of many ions in the oxygen isoelectronic sequence, the photoionisation of the ground state of neutral iron, the electron impact excitation of the fine-structure forbidden transitions within the 3p3ground configuration of CℓIII, Ar IV and K V, and the mass-production of radiative data for ions in the oxygen and fluorine isoelectronic sequences, as part of the international Opacity Project.

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