NDLI: The Quadrature Discretization Method (QDM) in the solution of the Schrödinger equation

Content Provider	Springer Nature Link
Author	Chen, Heli Shizgal, Bernie D.
Copyright Year	1998
Abstract	The Quadrature Discretization Method (QDM) is employed in the solution of several one‐dimensional Schrödinger equations that have received considerable attention in the literature. The QDM is based on the discretization of the wave function on a grid of points that coincide with the points of a quadrature. The quadrature is based on a set of non‐classical polynomials orthogonal with respect to a weight function. For a certain class of problems with potentials of the form that occur in supersymmetric quantum mechanics, the ground state wavefunction is known. In the present paper, the weight functions that are used are related to the ground state wavefunctions if known, or some approximate form. The eigenvalues and eigenfunctions of four different potential functions discussed extensively in the literature are calculated and the results are compared with published values.
Starting Page	321
Ending Page	343
Page Count	23
File Format	PDF
ISSN	02599791
Journal	Journal of Mathematical Chemistry
Volume Number	24
Issue Number	4
e-ISSN	15728897
Language	English
Publisher	Kluwer Academic Publishers-Plenum Publishers
Publisher Date	1998-01-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Math. Applications in Chemistry Physical Chemistry Theoretical and Computational Chemistry
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Chemistry

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The Quadrature Discretization Method (QDM) in the solution of the Schrödinger equation