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Bulletin of the Korean Chemical Society (BKCS)

ISSN 0253-2964(Print)
ISSN 1229-5949(Online)
Volume 34, Number 1
BKCSDE 34(1)
January 20, 2013

Title	General Orthogonality for Orthogonal Polynomials
Author	Hosung Sun
Keywords	Orthogonality, Solvable potentials, Orthogonal polynomials
Abstract	The bound state wave functions for all the known exactly solvable potentials can be expressed in terms of orthogonal polynomials because the polynomials always satisfy the boundary conditions with a proper weight function. The orthogonality of polynomials is of great importance because the orthogonality characterizes the wave functions and consequently the quantum system. Though the orthogonality of orthogonal polynomials has been known for hundred years, the known orthogonality is found to be inadequate for polynomials appearing in some exactly solvable potentials, for example, Ginocchio potential. For those potentials a more general orthogonality is defined and algebraically derived. It is found that the general orthogonality is valid with a certain constraint and the constraint is very useful in understanding the system.
Page	197 - 200
Full Text	PDF

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