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.author | Harrison, Halstead | en_US |
dc.contributor.author | Bernstein, Richard B. | en_US |
dc.date.accessioned | 2010-05-06T21:49:24Z | |
dc.date.available | 2010-05-06T21:49:24Z | |
dc.date.issued | 1963-05-01 | en_US |
dc.identifier.citation | Harrison, 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.uri | https://hdl.handle.net/2027.42/70222 | |
dc.description.abstract | A 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.extent | 3102 bytes | |
dc.format.extent | 496025 bytes | |
dc.format.mimetype | text/plain | |
dc.format.mimetype | application/pdf | |
dc.publisher | The American Institute of Physics | en_US |
dc.rights | © The American Institute of Physics | en_US |
dc.title | Iterative Method for Solution of the One‐Dimensional Wave Equation: Eigenvalues and Eigenfunctions for L‐J (12, 6) and Exponential (α, 6) Interatomic Potentials | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Physics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Chemistry Department, University of Michigan, Ann Arbor, Michigan | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/70222/2/JCPSA6-38-9-2135-1.pdf | |
dc.identifier.doi | 10.1063/1.1733945 | en_US |
dc.identifier.source | The Journal of Chemical Physics | en_US |
dc.identifier.citedreference | A. D. McLean, A. Weiss, and M. Yoshimine, Rev. Mod. Phys. 32, 211 (1960). | en_US |
dc.identifier.citedreference | D. Steele, E. R. Lippincott, and J. T. Vanderslice, Rev. Mod. Phys. 34, 239 (1962). | en_US |
dc.identifier.citedreference | F. A. Morse and R. B. Bernstein, J. Chem. Phys. 37, 2019 (1962). | en_US |
dc.identifier.citedreference | R. Helbing and H. Pauly, Z. Physik (to be published). | en_US |
dc.identifier.citedreference | H. Pauly, Z. Naturforsc. 15A, 277 (1960). | en_US |
dc.identifier.citedreference | H. W. Woolley, J. Chem. Phys. 37, 1307 (1962). | en_US |
dc.identifier.citedreference | D. R. Hartree, Proc. Cambridge Phil. Soc. 24, 105 (1928). | en_US |
dc.identifier.citedreference | R. 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.citedreference | For conventions see: D. McCracken, Digital Computer Programming (John Wiley & Sons, Inc., New York, 1951). | en_US |
dc.identifier.citedreference | P. M. Morse, Phys. Rev. 34, 57 (1929); see also the remarks of D. Ter Haar, 70, 222 (1946). | en_US |
dc.identifier.citedreference | N. Bernardes and H. Primakoff, J. Chem. Phys. 30, 691 (1959). | en_US |
dc.identifier.citedreference | See P. Swan, Proc. Roy. Soc. (London) A228, 10 (1955). | en_US |
dc.identifier.citedreference | R. B. Bernstein, J. Chem. Phys. 33, 795 (1960). | en_US |
dc.identifier.citedreference | R. E. Langer, Phys. Rev. 51, 669 (1937). | en_US |
dc.identifier.citedreference | Should we then label the method WKBJL? The modification was recognized by Kramers as early as 1926, however. See the remarks of Beckel.16 | en_US |
dc.identifier.citedreference | C. L. Beckel and J. Nakhleh, Phys. Rev. (to be published). | en_US |
dc.identifier.citedreference | J. L. Dunham, Phys. Rev. 41, 721 (1932). | en_US |
dc.identifier.citedreference | The 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.owningcollname | Physics, Department of |
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