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Advances in Mathematics Scientific Journal

MORSE POTENTIAL IN NONCOMMUTATIVE QUANTUM MECHANICS FRAMEWORK

A.H. Nadhira, M.S. Nurisya, K.T. Chan

Published Dec 18, 2020• 1 citation
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Abstract

Adv. Math. Sci. J. Vol. 9, No. 12 Open Access MORSE POTENTIAL IN NONCOMMUTATIVE QUANTUM MECHANICS FRAMEWORK A.H. Nadhira, M.S. Nurisya, and K.T. Chan DOI: https://doi.org/10.37418/amsj.9.12.73 Full Text Abstract Abstract Morse potential is one of the well-known exact solvable potentials which attracts many applications in quantum mechanics especially in quantum chemistry. Unlike harmonic … page AMSJ9-N12-73 Read More »

DOI
10.37418/amsj.9.12.73

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Adv. Math. Sci. J. Vol. 9, No. 12 Open Access MORSE POTENTIAL IN NONCOMMUTATIVE QUANTUM MECHANICS FRAMEWORK A.H. Nadhira, M.S. Nurisya, and K.T. Chan DOI: https://doi.org/10.37418/amsj.9.12.73 Full Text Abstract Abstract Morse potential is one of the well-known exact solvable potentials which attracts many applications in quantum mechanics especially in quantum chemistry. Unlike harmonic … page AMSJ9-N12-73 Read More »
Morse oscillator is one of the known solvable potentials which attracts many applications in quantum mechanics especially in quantum chemistry. One of the interesting results of this study is the generation of ladder operators for Morse potential. The operators are a representation of the shifting energy levels of the states exhibited by the wavefunction. From this result, we manipulate and deform the operators in such a way that it gives a noncommutative property to promote noncommutative quantum mechanics (NCQM). The resultant NC feature can be shown in the spatial coordinates and finally the Hamiltonian. In this study, we consider two-dimensional Morse potential where the ladder operators are in the form of the corresponding 2D Morse.
Previous article Next article Solvable Models in Quantum Mechanics (S. Albeverio, F. Gesztesy, R. Hoegh-Krohn, and H. Holden)F. H. BrownellF. H. Brownellhttps://doi.org/10.1137/1032018PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] H. Weyl, Ramifications, old and new, of the eigenvalue problem, Bull. Amer. Math. Soc., 56 (1950), 115–139 11,666i 0041.21003 CrossrefISIGoogle Scholar[2] F. H. Brownell, Spectrum of the static potential Schrödinger equation over $E\sb n$, Ann. of Math. (2), 54 (1951), 554–594 13,847a 0044.42703 CrossrefISIGoogle Scholar[3] F. A. Berezin and , L. D. Faddeev, A remark on Schrödinger's equation with a singular potential, Soviet Math. Dokl., 2 (1961), 372–375 0117.06601 Google Scholar[4] C. N. Friedman, Perturbations of the Schröedinger equation by potentials with small support, J. Functional Analysis, 10 (1972), 346–360 10.1016/0022-1236(72)90033-X 49:5529 0235.35009 CrossrefGoogle Scholar[5] F. H. Brownell, Real variables and Hilbert space operators for scientists, University Microfilms International, Ann Arbor, MI, 1978 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails On the relation between two different methods to treat Hamiltonians with point interactionsIntegral Equations and Operator Theory, Vol. 14, No. 3 Cross Ref Volume 32, Issue 1| 1990SIAM Review History Published online:18 July 2006 InformationCopyright © 1990 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1032018Article page range:pp. 160-167ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics