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A new method for approximate solution of one-dimensional Schrödinger equations

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Summary

A general method for approximate solution of one-dimensional Schrödinger equations with a wide range of square-integrable potentials is described. The potential is expanded in terms of either Jacobi or Bessel functions of argument exp(-r). This allows the Schrödinger equation to be solved by the Frobenius method. In the absence of super-computing power the input requirement of a large number of significant figures was handled by an algebraic computing package, for illustrative purposes. A sum of Gaussian wells and a Morse potential are treated as examples.

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References

  1. Compare Footnote in: French AP, Taylor EF (1978) An introduction to quantum physics, Thomas Nelson & Sons, p 394

  2. Dunham JL (1932) Phys Rev 41:713

    Google Scholar 

  3. Pauling L, Wilson EB (1935) Introduction to quantum mechanics, McGraw-Hill, p 198–203

  4. Flügge S (1974) Practical quantum mechanics. Springer-Verlag

  5. Hartree DR (1928) Proc Camb Phil Soc 24:105; Hartree DR (1932) Mem Manchester Phil Soc 77:91; Richardson RGD (1917) Trans Am Math Soc 18:489; Courant R, Friedrichs K, Leary H (1928) Math Ann 100:32; Kimball GE, Shortley GA (1934) Phys Rev 45:815

    Google Scholar 

  6. Bose SK, Varma N (1990) Phys Lett A 147:85

    Google Scholar 

  7. de Souza Dutra A (1988) Phys Lett A 131:319

    Google Scholar 

  8. Aly HH, Barut AO (1990) Phys Lett A 145:299

    Google Scholar 

  9. Kanshal RS (1989) Phys Lett A 142:57

    Google Scholar 

  10. Abramowitz M, Stegun IA (eds) (1972) Handbook of mathematical functions. Dover, NY; Gradsteyn IS, Ryzhik IM (1980) Tables of integrals, series and products. Academic Press, NY p 307, 930

    Google Scholar 

  11. Titchmarsh EC (1962) Eigenfunction expansions, Parts I and II. Clarendon Press, Oxford

    Google Scholar 

  12. Ince EL (1956) Ordinary differential equations. Dover, NY, p 396–403

    Google Scholar 

  13. Milne-Thomson LM (1933) The calculus of finite differences. MacMillan, London, p 380

    Google Scholar 

  14. Coddington EA (1961) An introduction to ordinary differential equations. Prentice-Hall, NY p 143–166

    Google Scholar 

  15. Travlos SD, Boeyens JCA (1991) J Chem Phys 95:4241

    Google Scholar 

  16. Wolfram S (1988) A system for doing mathematics by computer. Addison-Wesley, NY

    Google Scholar 

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  1. S. don Travlos

    Present address: Department of Chemistry, UNISA, Pretoria, South Africa

Authors and Affiliations

  1. Department of Chemistry, University of the Witwatersrand, P.O. WITS, 2050, Johannesburg, South Africa

    S. don Travlos & Jan C. A. Boeyens

Authors
  1. S. don Travlos
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  2. Jan C. A. Boeyens
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don Travlos, S., Boeyens, J.C.A. A new method for approximate solution of one-dimensional Schrödinger equations. Theoret. Chim. Acta 87, 453–464 (1994). https://doi.org/10.1007/BF01127808

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  • DOI: https://doi.org/10.1007/BF01127808

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