Skip to main content
SpringerLink
Log in

Restrictions on second order response properties of quantum states

  • Brief Communication
  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

Abstract

We distinguish two extreme classes of perturbation problems depending on the signs of second-order response properties. The first class refers to a positive value of the same for any state, and is overwhelmingly more probable. The other category offers all-but-one negative values, or at least some negative values for highly excited states. The classes are seen to differ in reproducing results of finite-dimensional matrix Hamiltonian perturbations, allowing the emergence of a type of sum rule. A few analytical findings are employed for direct demonstration. The outcomes provide notable restrictions on second order response properties of quantum states.

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

References

  1. J.O. Hirschfelder, W. Byers-Brown, S.T. Epstein, Adv. Quantum Chem. 1, 255 (1964)

    Article  CAS  Google Scholar 

  2. C.H. Wilcox (ed.), Perturbation Theory and Its Applications to Quantum Mechanics (Wiley, New York, 1966)

  3. M. Reed, B. Simon, Methods of Modern Mathematical Physics, vol. 4 (Academic, New York, 1978)

    Google Scholar 

  4. F. Gieres, Rep. Prog. Phys. 63, 1893 (2000)

    Article  CAS  Google Scholar 

  5. C.E. Reid, Int. J. Quantum Chem. 1, 521 (1967)

    Article  CAS  Google Scholar 

  6. R.J. Swenson, S.H. Danforth, J. Chem. Phys. 573, 1734 (1972)

    Article  Google Scholar 

  7. N. Bera, K. Bhattacharyya, J.K. Bhattacharjee, J. Phys. A Math. Theor. 41, 045301 (2008)

    Article  Google Scholar 

  8. J. Killingbeck, Phys. Lett. A 65, 87 (1978)

    Article  Google Scholar 

  9. H.A. Mavromatis, Int. J. Comput. Math. 50, 119 (1993)

    Article  Google Scholar 

  10. H.A. Mavromatis, Int. J. Math. Educ. Sci. Technol. 26, 267 (1995)

    Google Scholar 

  11. F.M. Fern’andez, Int. J. Math. Educ. Sci. Technol. 30, 405 (1999)

    Article  Google Scholar 

  12. M. Traini, Eur. J. Phys. 17, 30 (1996)

    Article  CAS  Google Scholar 

  13. D. M. Bishop, in Pauling’s Legacy, Modern Modelling of the Chemical Bond, Eds. Z. B. Maksic, W. J. Orville-Thomas (Elsevier, Amsterdam, 1999)

  14. M.I. Bhatti, K.D. Coleman, W.F. Perger, Phys. Rev. A 68, 044503 (2003)

    Article  Google Scholar 

  15. S.H. Patil, J. Chem. Phys. 83, 5764 (1985)

    Article  CAS  Google Scholar 

  16. J. Mitroy, M.S. Safronova, C.W. Clark, J. Phys. B: At. Mol. Opt. Phys. 43, 202001 (2010)

    Article  Google Scholar 

  17. V. Koch, D. Andrae, Theor. Chem. Acc. 114, 380 (2005)

    Article  CAS  Google Scholar 

  18. U. Hohm, A.J. Thakkar, J. Phys. Chem. A 116, 697 (2012)

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Chemistry, University of Calcutta, Kolkata, 700009, India

    Kamal Bhattacharyya

Authors
  1. Kamal Bhattacharyya
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kamal Bhattacharyya.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bhattacharyya, K. Restrictions on second order response properties of quantum states. J Math Chem 52, 1639–1646 (2014). https://doi.org/10.1007/s10910-014-0355-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10910-014-0355-8

Keywords

Search

Navigation