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Iterative Method for Solution of the One‐Dimensional Wave Equation: Eigenvalues and Eigenfunctions for L‐J (12, 6) and Exponential (α, 6) Interatomic Potentials
dc.contributor.authorHarrison, Halsteaden_US
dc.contributor.authorBernstein, Richard B.en_US
dc.date.accessioned2010-05-06T21:49:24Z
dc.date.available2010-05-06T21:49:24Z
dc.date.issued1963-05-01en_US
dc.identifier.citationHarrison, Halstead; Bernstein, Richard B. (1963). "Iterative Method for Solution of the One‐Dimensional Wave Equation: Eigenvalues and Eigenfunctions for L‐J (12, 6) and Exponential (α, 6) Interatomic Potentials." The Journal of Chemical Physics 38(9): 2135-2143. <http://hdl.handle.net/2027.42/70222>en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/70222
dc.description.abstractA method of direct numerical integration of the one‐dimensional wave equation is described and illustrated by calculations of the radial wavefunctions, vibrational energy levels, and numbers of bound states for diatomic molecules. Within the validity of the Born—Oppenheimer approximation, the procedure yields arbitrarily accurate eigenvalues. Several potentials involving long‐range, inverse‐sixth‐power attractions are examined. Results are compared with those from the first‐order WKBJ integral and with the Dunham form of the second‐order WKBJ approximation.en_US
dc.format.extent3102 bytes
dc.format.extent496025 bytes
dc.format.mimetypetext/plain
dc.format.mimetypeapplication/pdf
dc.publisherThe American Institute of Physicsen_US
dc.rights© The American Institute of Physicsen_US
dc.titleIterative Method for Solution of the One‐Dimensional Wave Equation: Eigenvalues and Eigenfunctions for L‐J (12, 6) and Exponential (α, 6) Interatomic Potentialsen_US
dc.typeArticleen_US
dc.subject.hlbsecondlevelPhysicsen_US
dc.subject.hlbtoplevelScienceen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationumChemistry Department, University of Michigan, Ann Arbor, Michiganen_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/70222/2/JCPSA6-38-9-2135-1.pdf
dc.identifier.doi10.1063/1.1733945en_US
dc.identifier.sourceThe Journal of Chemical Physicsen_US
dc.identifier.citedreferenceA. D. McLean, A. Weiss, and M. Yoshimine, Rev. Mod. Phys. 32, 211 (1960).en_US
dc.identifier.citedreferenceD. Steele, E. R. Lippincott, and J. T. Vanderslice, Rev. Mod. Phys. 34, 239 (1962).en_US
dc.identifier.citedreferenceF. A. Morse and R. B. Bernstein, J. Chem. Phys. 37, 2019 (1962).en_US
dc.identifier.citedreferenceR. Helbing and H. Pauly, Z. Physik (to be published).en_US
dc.identifier.citedreferenceH. Pauly, Z. Naturforsc. 15A, 277 (1960).en_US
dc.identifier.citedreferenceH. W. Woolley, J. Chem. Phys. 37, 1307 (1962).en_US
dc.identifier.citedreferenceD. R. Hartree, Proc. Cambridge Phil. Soc. 24, 105 (1928).en_US
dc.identifier.citedreferenceR. A. Buckingham and J. W. Fox, Proc. Roy. Soc. (London) A267, 102 (1962); a procedure very similar to ours is applied to nuclear bound states by R. S. Caswell, National Bureau of Standards Tech. Note #159 (1962).en_US
dc.identifier.citedreferenceFor conventions see: D. McCracken, Digital Computer Programming (John Wiley & Sons, Inc., New York, 1951).en_US
dc.identifier.citedreferenceP. M. Morse, Phys. Rev. 34, 57 (1929); see also the remarks of D. Ter Haar, 70, 222 (1946).en_US
dc.identifier.citedreferenceN. Bernardes and H. Primakoff, J. Chem. Phys. 30, 691 (1959).en_US
dc.identifier.citedreferenceSee P. Swan, Proc. Roy. Soc. (London) A228, 10 (1955).en_US
dc.identifier.citedreferenceR. B. Bernstein, J. Chem. Phys. 33, 795 (1960).en_US
dc.identifier.citedreferenceR. E. Langer, Phys. Rev. 51, 669 (1937).en_US
dc.identifier.citedreferenceShould we then label the method WKBJL? The modification was recognized by Kramers as early as 1926, however. See the remarks of Beckel.16en_US
dc.identifier.citedreferenceC. L. Beckel and J. Nakhleh, Phys. Rev. (to be published).en_US
dc.identifier.citedreferenceJ. L. Dunham, Phys. Rev. 41, 721 (1932).en_US
dc.identifier.citedreferenceThe nonconvergence for r−6r−6 potentials is shared by a recent second‐order perturbation calculation: A. M. Shorb, R. Schroeder, and E. R. Lippincott, J. Chem. Phys. 37, 1043 (1962).en_US
dc.owningcollnamePhysics, Department of


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