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Generalized potentials: Free particle, harmonic, and Morse partner potentials
Author(s) -
Morales J.,
Peña J. J.,
Ovando G.,
Gaftoi V.
Publication year - 1999
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/(sici)1097-461x(1999)71:6<465::aid-qua3>3.0.co;2-t
Subject(s) - isospectral , hamiltonian (control theory) , morse potential , generalization , harmonic potential , harmonic oscillator , morse code , free particle , physics , quantum , particle in a box , eigenvalues and eigenvectors , quantum mechanics , classical mechanics , mathematical physics , statistical physics , mathematics , mathematical analysis , computer science , mathematical optimization , telecommunications
In this work, we propose a very simple procedure to find the partner to specific potentials. According to our method, partner potentials are those obtained in the generalization of standard potentials, for which they are generalized potentials whose Hamiltonian match the so‐called isospectral Hamiltonian. The proposed approach is straightforward and basically takes into consideration the use of three well‐established relationships: The first one is used to identify the particular potential; the second, to find the adjoint or modified potential; and the third, to obtain the corresponding generalized or partner potential. As a useful application of the proposed procedure, we give explicitly the generalized and modified free‐particle, harmonic oscillator, and Morse one‐dimensional potentials. As expected, it is shown that the adjoint and partner potentials are isospectral with respect to the particular or former potential. This procedure can be easily applied to the generalization of any other known potential, as well as to obtain new potentials that can be advantageously used for modeling important quantum interactions. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 465–472, 1999