Skip to main content
SpringerLink
Log in

Toward chemical applications of Heaviside Operational Ansatz: exact solution of radial Schrodinger equation for nonrelativistic N-particle system with pairwise \({\frac{1}{r_{ij}}}\) radial potential in quantum phase space

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

An Erratum to this article was published on 22 July 2008

Abstract

This brief note presents the exact analytical solution of an example class of dynamical systems, realized by differential equations. These problems occur in quantum mechanics and their generalizations in theoretical physics, but they particularly find application to chemical systems. Addressed is the exact analytical solution of the radial Schrodinger equation for the nonrelativistic N-particle system with pairwise \({\frac{1}{r_{ij}}}\) radial potential dynamics in the quantum phase space representation (QPSR) (Torres-Vega, Frederick, J. Chem. Phys. 98 3103, 1993). Applying the formal symbolic solution scheme Heaviside Operational Ansatz (heretofore, HOA) put forward in (Electron. J. Theor. Phys. 1 , 10–16, 2004), reduces solution of the radial Schrodinger equation to exact quadratures.

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

  • Torres-Vega Go. and Frederick J.H. (1993). J. Chem. Phys. 98: 3103

    Article  CAS  Google Scholar 

  • Li Q.S. and Lu J. (2000). J. Chem. Phys. 113(11): 4565–4571

    Article  CAS  Google Scholar 

  • Hu X.-G. and Li Q.S. (1999). J. Phys. A Math. Gen. 32(1): 139–146

    Article  CAS  Google Scholar 

  • Li Q.S. and Lu J. (2001). Chem. Phys. Lett. 336(1,2): 118–122

    Article  CAS  Google Scholar 

  • Li Q.S., Wei G.M. and Lu L.Q. (2004). Phys. Rev. A Atom. Mol. Opt. Phys. 70(2): 022105/1–022105/5

    CAS  Google Scholar 

  • Yariv A. (1982). Theory and Applications of Quantum Mechanics. Wiley and Sons, NY

    Google Scholar 

  • Moss R.E. (1973). Advanced Molecular Quantum Mechanics. Wiley and Sons, NY

    Google Scholar 

  • I. Lindgren, in Lecture Notes in Chemistry, vol. 52: Many-Body Methods in Quantum Chemistry, ed. by U. Kaldor (Springer, Berlin, 1989), pp. 293–306

  • Simpao V.A. (2006). Majorana special issue. Electron. J. Theor. Phys. 3(10): 239

    Google Scholar 

  • V.A. Simpao, Exact analysis of He atom via Heaviside operational Ansatz (in preparation)

  • V.A. Simpao, Exact analysis of H Dimer via Heaviside operational Ansatz (in preparation)

  • G.E. Roberts, H. Kaufmann, Table of Laplace Transforms (W.B. Saunders, 1966)

  • I. Sneddon, The Use of Integral Transforms (McGraw-Hill, 1972)

Download references

Author information

Authors and Affiliations

  1. Mathematical Consultant Services, 108 Hopkinsville Street, Greenville, KY, 42345, USA

    Valentino A. Simpao

Authors
  1. Valentino A. Simpao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Valentino A. Simpao.

Additional information

An erratum to this article can be found at http://dx.doi.org/10.1007/s10910-008-9400-9

Rights and permissions

Reprints and permissions

About this article

Cite this article

Simpao, V.A. Toward chemical applications of Heaviside Operational Ansatz: exact solution of radial Schrodinger equation for nonrelativistic N-particle system with pairwise \({\frac{1}{r_{ij}}}\) radial potential in quantum phase space. J Math Chem 45, 129–140 (2009). https://doi.org/10.1007/s10910-008-9372-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10910-008-9372-9

Keywords

Search

Navigation