Ladder operator relations for hypergeometric functions

Laha, U.; Bhattacharyya, C; Talukdar, B.

doi:10.1088/0305-4470/19/9/003

Cited by 12 publications

(3 citation statements)

References 7 publications

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“…4 These relations are also given in [22]. 5 These relations had also been derived in [19] in a complicated manner. Using the differential equation for 1 F 1 (a, c; x) to eliminate the d 2 dx 2 termwefinallyobtain(seefootnote5)…”

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confidence: 99%

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Ladder operators and a dynamicalSU(2) group symmetry of the hydrogen atom system

Devi

Singh²

2014

Phys. Scr.

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By invoking a standard variable transformation x → y ≡ x 2 that connects the eigenvalue problems of the hydrogen atom system (Coulomb potential) and the Kratzer oscillator system, we obtain a system of ladder operators ± nl (l = 0, 1, 2, . . . , n − 1) that connect the degenerate energy eigenstates (belonging to different l-values) of the hydrogen atom system. Using such quantum number specific operators as the precursors, we develop a general method of constructing quantum number independent ladder operators P± ; and then investigate the general conditions for these operators to form a realization of the su(2) algebra. In the process, we demonstrate that, in general, a finite-dimensional linear vector space carries a realization of the su(2) algebra. Applying the method to the case at hand, we show that for the hydrogen atom system the operators P± and P0 ≡ 1 2 [ P+ , P− ] form an su(2) algebra. The Hamiltonian is identified with the Casimir operator of the algebra, thereby revealing a dynamical SU(2) group symmetry of the hydrogen atom system.

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Section: Discussionmentioning

confidence: 99%

“…In appendix B we deduce the following two recurrence relations of the confluent hypergeometric functions (equations (B.7) and (B.8)) (see also [19])…”

Section: Ladder Operators For the H-atommentioning

confidence: 99%

Ladder operators and a dynamicalSU(2) group symmetry of the hydrogen atom system

Devi

Singh²

2014

Phys. Scr.

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“…These relations are also given in[16] 6. These two relations were also derived in[17] in a complicated way.…”

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confidence: 99%

Dynamic parameterization and ladder operators for the Kratzer molecular potential

Devi¹,

Singh²

2014

Phys. Scr.

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Introducing independent parameters k and δ to represent the strength of the attractive and repulsive components, respectively, we write the Kratzer molecular potential asThis parameterisation is not only natural, but also convenient for the construction of ladder operators for the system. Adopting the straightforward method of deriving recurrence relations among confluent hypergeometric functions, we construct seven pairs of ladder operators for the Kratzer potential system. Detailed analysis of the laddering actions of these operators is given to show that they connect eigenstates of equal energy but belong to a hierarchy of Kratzer potential systems corresponding to different values of the parameters k and δ. Significantly, it is pointed out that it may not be possible to construct, in the position representation, a ladder operator which would connect different eigenstates belonging to the same potential δ V k ( , ). Transition to the hydrogen atom case is discussed. A number (14 altogether) of functional relations among the confluent hypergeometric functions have been derived and reported separately in an appendix.

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