A unified recurrence operator method for obtaining normalized explicit wavefunctions for shape-invariant potentials

Jia, Chun‐Sheng; Wang, Xiao-Guo; Yao, Xiao-Ke; Chen, Pu-Chun; Xiao, Wei

doi:10.1088/0305-4470/31/20/013

Cited by 54 publications

(16 citation statements)

References 9 publications

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“…Using the recursion operator approach [55,56], we can determine the excited state upper components from the superpotential W(r) given in Eq. (20) and the ground-state upper component, F 0,j (r) given in Eq.…”

Section: P-spin Symmetry Limitmentioning

confidence: 99%

Tensor coupling and relativistic spin and pseudospin symmetries of the Pöschl–Teller-like potential

2014

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In this research, we have been obtained the Dirac equation for second Pöschl-Teller-like potential including a Coulomb-like tensor interaction with arbitrary spin-orbit coupling quantum number j. Under the condition of spin and pseudospin (p-spin) symmetries, we use the basic concept of the supersymmetric shape invariance formulism in quantum mechanics and the function analysis method to obtain energy eigenvalues and corresponding two-component spinors of the Dirac particle. We have also shown that tensor interaction removes degeneracies between spin and p-spin doublets. Some numerical results are also given.

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Section: P-spin Symmetry Limitmentioning

confidence: 99%

Tensor coupling and relativistic spin and pseudospin symmetries of the Pöschl–Teller-like potential

2014

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“…In terms of the superpotential W (r ) given in expression (15) and the groundstate wave function u 0,J (r ) given in expression (22), we can yield the excited state wave functions by employing the explicit recursion operator approach [57,58]. The unnormalized wave functions are given by [57] …”

Section: Bound State Solutionsmentioning

confidence: 99%

D-dimensional energies for scandium monoiodide

Guo

Jia

2014

J Math Chem

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We solve the Schrödinger equation with the Morse potential energy model in D spatial dimensions. The bound state rotation-vibrational energy spectra have been obtained by using the supersymmetric shape invariance approach. For a fixed vibrational quantum number and various rotational quantum numbers, the energies for the X 1 + state of ScI molecule increase as D increases. We observe that the behavior of the vibrational energies in higher dimensions remains similar to that of the three-dimensional system. The dimensional scaling method resembles a translation transformation from the higher dimensions to the actual three dimensions.

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“…The excited state wavefunctions can be easily determined from the usual approach in supersymmetric quantum mechanics [9] and the normalization coefficients for each quantum state wave function can be analytically worked out using the explicit recurrence relation given in a recent work [31].…”

Section: Exactly Solvable Casementioning

confidence: 99%

Supersymmetry and the relationship between a class of singular potentials in arbitrary dimensions

Gönül

Özer

Koçak

et al. 2001

J. Phys. A: Math. Gen.

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A unified recurrence operator method for obtaining normalized explicit wavefunctions for shape-invariant potentials

Cited by 54 publications

References 9 publications

Tensor coupling and relativistic spin and pseudospin symmetries of the Pöschl–Teller-like potential

Tensor coupling and relativistic spin and pseudospin symmetries of the Pöschl–Teller-like potential

D-dimensional energies for scandium monoiodide

Supersymmetry and the relationship between a class of singular potentials in arbitrary dimensions

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