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Arista J, Demni N. Explicit Expressions of the Hua--Pickrell Semigroup. THEORY OF PROBABILITY AND ITS APPLICATIONS 2022. [DOI: 10.1137/s0040585x97t990885] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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A New Constructive Method for Solving the Schrödinger Equation. Symmetry (Basel) 2021. [DOI: 10.3390/sym13101879] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
In this paper, a new method for the exact solution of the stationary, one-dimensional Schrödinger equation is proposed. Application of the method leads to a three-parametric family of exact solutions, previously known only in the limiting cases. The method is based on solutions of the Ricatti equation in the form of a quadratic function with three parameters. The logarithmic derivative of the wave function transforms the Schrödinger equation to the Ricatti equation with arbitrary potential. The Ricatti equation is solved by exploiting the particular symmetry, where a family of discrete transformations preserves the original form of the equation. The method is applied to a one-dimensional Schrödinger equation with a bound states spectrum. By extending the results of the Ricatti equation to the Schrödinger equation the three-parametric solutions for wave functions and energy spectrum are obtained. This three-parametric family of exact solutions is defined on compact support, as well as on the whole real axis in the limiting case, and corresponds to a uniquely defined form of potential. Celebrated exactly solvable cases of special potentials like harmonic oscillator potential, Coulomb potential, infinite square well potential with corresponding energy spectrum and wave functions follow from the general form by appropriate selection of parameters values. The first two of these potentials with corresponding solutions, which are defined on the whole axis and half axis respectively, are achieved by taking the limit of general three-parametric solutions, where one of the parameters approaches a certain, well-defined value.
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Krasnoshchekov SV, Chang X. Ladder operators for Morse oscillator and a perturbed vibrational problem. INT REV PHYS CHEM 2019. [DOI: 10.1080/0144235x.2019.1593583] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
| | - Xuanhao Chang
- School of Nuclear Science and Engineering, Tomsk Polytechnic University, Tomsk, Russia
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Jia CS, Dai JW, Zhang LH, Liu JY, Zhang GD. Molecular spinless energies of the modified Rosen–Morse potential energy model in higher spatial dimensions. Chem Phys Lett 2015. [DOI: 10.1016/j.cplett.2014.11.039] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Jia CS, Peng XL, He S. Molecular Spinless Energies of the Modified Rosen-Morse Potential Energy Model. B KOREAN CHEM SOC 2014. [DOI: 10.5012/bkcs.2014.35.9.2699] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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Abstract
We solve the Schrödinger equation with the improved Rosen−Morse potential energy model in D spatial dimensions. The D-dimensional rotation-vibrational energy spectra have been obtained by using the supersymmetric shape invariance approach. The energies for the 33[Formula: see text]g+ state of the Cs2 molecule and the 51Δg state of the Na2 molecule increase as D increases in the presence of fixed vibrational quantum number and various rotational quantum numbers. We observe that the change in behavior of the vibrational energies in higher dimensions remains similar to that of the three-dimensional system.
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Affiliation(s)
- Xue-Tao Hu
- State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, People’s Republic of China
- School of Petroleum Engineering, Southwest Petroleum University, Chengdu 610500, People’s Republic of China
| | - Lie-Hui Zhang
- State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, People’s Republic of China
| | - Chun-Sheng Jia
- State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, People’s Republic of China
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Callen BD, Volkas RR. Solutions for intersecting domain walls with internal structure in six dimensions from a Z2×Z2-invariant action. Int J Clin Exp Med 2013. [DOI: 10.1103/physrevd.87.116002] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Callen BD, Volkas RR. Fermion masses and mixing in a4+1dimensionalSU(5)domain-wall brane model. Int J Clin Exp Med 2011. [DOI: 10.1103/physrevd.83.056004] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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De R, Dutt R, Sukhatme U. Mapping of shape invariant potentials under point canonical transformations. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/25/13/013] [Citation(s) in RCA: 156] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Khare A, Sukhatme UP. New shape-invariant potentials in supersymmetric quantum mechanics. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/26/18/003] [Citation(s) in RCA: 93] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Mesa ADS, Quesne C, Smirnov YF. Generalized Morse potential: Symmetry and satellite potentials. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/31/1/028] [Citation(s) in RCA: 64] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Engelfield MJ, Quesne C. Dynamical potential algebras for Gendenshtein and Morse potentials. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/24/15/023] [Citation(s) in RCA: 46] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Levai G. On some exactly solvable potentials derived from supersymmetric quantum mechanics. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/25/9/003] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Khare A, Sukhatme UP. Scattering amplitudes for supersymmetric shape-invariant potentials by operator methods. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/21/9/005] [Citation(s) in RCA: 116] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Barclay DT, Dutt R, Gangopadhyaya A, Khare A, Pagnamenta A, Sukhatme U. New exactly solvable Hamiltonians: Shape invariance and self-similarity. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1993; 48:2786-2797. [PMID: 9909928 DOI: 10.1103/physreva.48.2786] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Dutt R, Gangopadhyaya A, Khare A, Pagnamenta A, Sukhatme U. Semiclassical approach to quantum-mechanical problems with broken supersymmetry. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1993; 48:1845-1853. [PMID: 9909799 DOI: 10.1103/physreva.48.1845] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Jayannavar AM, Khare A. Propagators for shape-invariant singular potentials. Int J Clin Exp Med 1993; 47:4796-4797. [PMID: 10015483 DOI: 10.1103/physrevd.47.4796] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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De R, Dutt R, Sukhatme U. Path-integral solutions for shape-invariant potentials using point canonical transformations. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 46:6869-6880. [PMID: 9908017 DOI: 10.1103/physreva.46.6869] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Voronin AI. Neutron in the magnetic field of a linear conductor with current as an example of the two-dimensional supersymmetric problem. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1991; 43:29-34. [PMID: 9904750 DOI: 10.1103/physreva.43.29] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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