Skip to main content
SpringerLink
Log in

What mathematicians know about the solutions of Schrodinger Coulomb Hamiltonian. Should chemists care?

  • Original Paper
  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

Abstract

An attempt is made to determine the relationship between the full Schrödinger Coulomb Hamiltonian and the clamped nuclei form that is usually the basis of electronic structure calculations, without treating identical nuclei as distinguishable. It is concluded that it is not at present possible to establish such a relationship in a mathematically secure way.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R.G. Woolley, in Handbook of Molecular Physics and Quantum Chemistry, ed. by S. Wilson. Fundamentals, vol. 1, Part 7, Ch. 40 (John Wiley, Chichester, 2003), p. 679

  2. Kato T. (1951) Trans. Am. Math. Soc. 70, 212

    Article  Google Scholar 

  3. W. Thirring, in Schrödinger, Centenary Celebrations of a Polymath, ed. by C. W. Kilminster (Cambridge University Press, Cambridge, 1987), p. 65

  4. Kato T.(1957) Commun. Pure Appl. Math. 10: 151

    Article  Google Scholar 

  5. Reed M., Simon B. (1978) Methods of Modern Mathematical Physics, IV, Analysis of Operators. Academic Press, New York

    Google Scholar 

  6. Reed M., Simon B. (1980) Methods of Modern Mathematical Physics, I, Functional Analysis, revised and enlarged edition. Academic Press, New York

    Google Scholar 

  7. Reed M., Simon B. (1975) Methods of Modern Mathematical Physics, II, Fourier Analysis, Self-Adjointness. Academic Press, New York

    Google Scholar 

  8. W. Thirring, A Course in Mathematical Physics, vol. 3. Quantum Mechanics of Atoms and Molecules, Tr. E. M. Harrell (Springer-Verlag, New York, 1981)

  9. J.-M. Combes, R. Seiler, in Quantum Dynamics of Molecules, ed. by R.G. Woolley (Plenum Press, New York, 1980), NATO ASI B57, p. 435.

  10. Zhislin G.M. (1960) Trudy Moskov Mat. Obsc. 9, 82

    Google Scholar 

  11. Lieb E.H., Loss M. (2003) Adv. Theor. Math. Phys. 7, 667

    Google Scholar 

  12. Uchiyama J. (1967) Publ. Res. Inst. Math. Sci. Kyoto A 2, 117

    Article  Google Scholar 

  13. Simon B. (1971) Quantum Mechanics for Hamiltonians Defined as Quadratic Forms. Princeton University Press, Princeton

    Google Scholar 

  14. Zhislin G.M. (1971) Theor. Math. Phys. 7, 571

    Article  Google Scholar 

  15. Nyden Hill R. (1977) . J. Math. Phys. 18: 2316

    Article  Google Scholar 

  16. Richard J.-M., Fröhlich J., Graf G.-M., Seifert M. (1993) . Phys. Rev. Lett. 71: 1332

    Article  CAS  Google Scholar 

  17. Ruskai M.B. (1990) . Ann. Inst. Henri Poincaré. 52, 397

    Google Scholar 

  18. Ruskai M.B. (1991) . Commun. Math. Phys. 137: 553

    Article  Google Scholar 

  19. Simon B. (1970) . Helv. Phys. Acta. 43, 607

    CAS  Google Scholar 

  20. Vugal’ter S.A., Zhislin G.M. (1977) . Theor. Math. Phys. 32, 602

    Article  Google Scholar 

  21. Evans W.D., Lewis R.T., Saito Y. (1992) . Phil. Trans. R. Soc. Lond. A 338, 113

    Article  Google Scholar 

  22. H. Weyl, The Theory of Groups and Quantum Mechanics, 2nd edn. Tr. H.P. Robertson (Dover, New York, 1931)

  23. Mackey G. (1963) The Mathematical Foundations of Quantum Mechanics. Benjamin, New York

    Google Scholar 

  24. Balslev E. (1972) . Ann. Phys. (NY) 73, 49

    Article  Google Scholar 

  25. R.G. Woolley, B.T. Sutcliffe, in Fundamental World of Quantum Chemistry, vol. 1, eds. by E.J. Brändas, E.S. Kryachko (Kluwer Academic, 2003), p. 21

  26. Born M., Oppenheimer J.R. (1927) . Ann. Phys. 84, 457

    Article  CAS  Google Scholar 

  27. Sutcliffe B.T., Woolley R.G. (2005) . Phys. Chem. Chem. Phys. 7: 3664

    Article  CAS  Google Scholar 

  28. Mead C.A. (1992) . Rev. Mod. Phys. 64, 51

    Article  CAS  Google Scholar 

  29. J.-M. Combes, P. Duclos, R. Seiler, in Rigorous Results in Atomic and Molecular Physics, ed. by G. Velo, A. Wightman (Plenum, New York, 1981), p. 185

  30. Klein M., Martinez A., Seiler R., Wang X.P. (1992) . Commun. Math. Phys. 143, 607

    Article  Google Scholar 

  31. Born M., Huang K. (1955) In Dynamical Theory of Crystal Lattices, Appendix 8. Oxford University Press, Oxford

    Google Scholar 

  32. Hagedorn G. (1980) Commun. Math. Phys. 77, 1

    Article  Google Scholar 

  33. Hagedorn G., Joye A. (2001) Commun. Math. Phys. 223, 583

    Article  Google Scholar 

  34. Hagedorn G. (1990) . Theor. Chim. Acta. 77, 163

    Article  CAS  Google Scholar 

  35. Schmelzer A., Murrell J.N. (1985) . Int. J. Quant. Chem. 28, 288

    Article  Google Scholar 

  36. Collins M.A., Parsons D.F. (1993) . J. Chem. Phys. 99: 6756

    Article  CAS  Google Scholar 

  37. Brown A., McCoy A.B., Braams B.B., Jin Z., Bowman J.M. (2004) . J. Chem. Phys. 121: 4105

    Article  CAS  Google Scholar 

  38. Weyl H. (1946) The Classical Groups: Their Invariants and Representations, 2nd edn. Princeton University, Princeton, p. 75

    Google Scholar 

  39. Helffer B., Sjöstrand J. (1984) . Commun. Partial Differ. Equations. 9, 337

    Article  Google Scholar 

  40. Katriel J., Paldus J., Pauncz R. (1985) . Int. J. Quant. Chem. 28, 181

    Article  Google Scholar 

  41. Katriel J. (2001) . J. Mol. Struct. (Theochem) 547: 1

    Article  CAS  Google Scholar 

  42. Eckart C. (1935) . Phys. Rev. 47, 552

    Article  CAS  Google Scholar 

  43. Longuet-Higgins H.C. (1963) . Mol. Phys. 6, 445

    Article  CAS  Google Scholar 

  44. Ezra G. (1982) . Symmetry properties of Molecules, Lecture Notes in Chemistry vol. 28. Springer, Berlin

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Chimie quantique et Photophysique, Universite Libre be Bruxelles, 1050, Bruxelles, Belgium

    Brian T. Sutcliffe

Authors
  1. Brian T. Sutcliffe
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Brian T. Sutcliffe.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sutcliffe, B.T. What mathematicians know about the solutions of Schrodinger Coulomb Hamiltonian. Should chemists care?. J Math Chem 44, 988–1008 (2008). https://doi.org/10.1007/s10910-008-9358-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10910-008-9358-7

Keywords

Search

Navigation