Skip to main content

A systematic semiempirical study of information inequalities for the vibrational levels of a diatomic molecule for the example of the ground electronic state of 7Li2

Abstract

A systematic study of the dependences of information inequalities relating the variance, Fisher information, and Shannon entropy power in the coordinate and momentum spaces (the Cramér–Rao, Stam, Bialynicki–Birula–Mycielsky–Beckner, and other inequalities) on the vibrational quantum number of a diatomic molecule is performed for the first time. These dependences are calculated for the ground electronic state of the 7Li2 molecule using the semiempirical data available in the literature on the many-parameter potential curve of this state. Specific features of these dependences have been analyzed, their essentially nonmonotonic behavior was revealed, and not only quantitative, but also qualitative, distinctions between these dependences were observed. These results were compared with the results of our calculation in the classical mechanics approximation, and significant (up to a factor of 3.5) discrepancies between these data were observed not only for low-lying, but also for highly excited vibrational levels that are close to the dissociation limit. The results obtained can be used in quantum informatics, analysis of an intramolecular structure and the interaction processes involving the vibrational states of diatomic molecules.

This is a preview of subscription content, access via your institution.

References

  1. 1.

    S. A. Astashkevich, Opt. Spectrosc. 117, 687 (2014).

    ADS  Article  Google Scholar 

  2. 2.

    Statistical Complexity, Ed. by K. D. Sen (Springer, New York, London, 2011).

  3. 3.

    L. Skála and V. Kapsa, Opt. Spectrosc. 103, 434 (2007).

    ADS  Article  Google Scholar 

  4. 4.

    S. Wehner and A. Winter, New J. Phys. 12, 025009 (2010).

    ADS  MathSciNet  Article  Google Scholar 

  5. 5.

    P. Busch and C. Shilladay, Phys. Rep. 435, 1 (2006).

    ADS  Article  Google Scholar 

  6. 6.

    G. M. Bosyk, M. Portesi, F. Holik, and A. Plastino, Phys. Scr. 87, 065002 (2013).

    ADS  Article  Google Scholar 

  7. 7.

    N. L. Guevara, R. P. Sagar, and R. O. Esquivel, Phys. Rev. A 67, 012507 (2003).

    ADS  Article  Google Scholar 

  8. 8.

    I. V. Toranzo, S. López-Rosa, R. O. Esquivel, and J. S. Dehesa, Phys. Rev. A 91, 062122 (2015).

    ADS  Article  Google Scholar 

  9. 9.

    W. Heisenberg, Z. Phys. 43, 172 (1927).

    ADS  Article  Google Scholar 

  10. 10.

    H. P. Robertson, Phys. Rev. 35, 667 (1930).

    Google Scholar 

  11. 11.

    E. Schrödinger, Sitzungsber. Preuss. Akad. Wiss. 19, 296 (1930).

    Google Scholar 

  12. 12.

    V. V. Dodonov, E. V. Kurmyshev, and V. I. Man’ko, Phys. Lett. A 79, 150 (1980).

    ADS  MathSciNet  Article  Google Scholar 

  13. 13.

    V. V. Dodonov, V. I. Man’ko, Tr. FIAN 183, 5 (1987).

    Google Scholar 

  14. 14.

    A. D. Sukhanov, Teor. Math. Phys. 132, 1277 (2002).

    Article  Google Scholar 

  15. 15.

    I. Bialynicki-Birula and J. Mycielsky, Comm. Math. Phys. 44, 129 (1975).

    ADS  MathSciNet  Article  Google Scholar 

  16. 16.

    W. Beckner, Ann. Math. 102, 159 (1975).

    MathSciNet  Article  Google Scholar 

  17. 17.

    J. I. de Vicente and J. Sánchez-Ruiz, Phys. Rev. A 77, 042110 (2008).

    ADS  Article  Google Scholar 

  18. 18.

    S. Zozor, M. Portesi, P. Sánchez-Moreno, and J. S. Dehesa, Phys. Rev. A 83, 052107 (2011).

    ADS  Article  Google Scholar 

  19. 19.

    M. A. Man’ko and V. I. Man’ko, Found. Phys. 41, 330 (2011).

    ADS  MathSciNet  Article  Google Scholar 

  20. 20.

    V. N. Chernega, O. V. Man’ko, and V. I. Man’ko, Found. Phys. 45, 783 (2015).

    ADS  MathSciNet  Article  Google Scholar 

  21. 21.

    E. Romera, P. Sánchez-Moreno, and J. S. Dehesa, Chem. Phys. Lett. 414, 468 (2005).

    ADS  Article  Google Scholar 

  22. 22.

    S. López-Rosa, J. Montero, P. Sánchez-Moreno, et al., J. Math. Chem. 49, 971 (2011).

    MathSciNet  Article  Google Scholar 

  23. 23.

    J. S. Dehesa, A. Martínez-Finkelshtein, and V. N. Sorokin, Mol. Phys. 104, 613 (2006).

    ADS  Article  Google Scholar 

  24. 24.

    J. S. Dehesa, A. Martínez-Finkelshtein, and V. N. Sorokin, Phys. Rev. A 66, 062109 (2002).

    ADS  Article  Google Scholar 

  25. 25.

    P. Sánchez-Moreno, A. R. Plastino, and J. S. Dehesa, J. Phys. A 44, 065301 (2011).

    ADS  MathSciNet  Article  Google Scholar 

  26. 26.

    A. Dembo, T. M. Cover, and J. A. Thomas, IEEE Trans. Inf. Theory 37, 1501 (1991).

    Article  Google Scholar 

  27. 27.

    R. J. Le Roy, C. C. Haugen, J. Tao, and H. Li, Mol. Phys. 109, 435 (2011).

    ADS  Article  Google Scholar 

  28. 28.

    L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 3: Quantum Mechanics: Non-Relativistic Theory (Nauka, Moscow, 1989, 4th ed.; Pergamon, New York, 1977, 3rd ed.).

    Google Scholar 

  29. 29.

    S. A. Astashkevich and B. P. Lavrov, Opt. Spectrosc. 100, 489 (2006).

    ADS  Article  Google Scholar 

  30. 30.

    S. A. Astashkevich, Opt. Spectrosc. 102, 175 (2007).

    ADS  Article  Google Scholar 

  31. 31.

    S. A. Astashkevich and B. P. Lavrov, Opt. Spectrosc. 86, 845 (1999).

    ADS  Google Scholar 

  32. 32.

    S. A. Astashkevich and B. P. Lavrov, Opt. Spectrosc. 92, 818 (2002).

    ADS  Article  Google Scholar 

  33. 33.

    S. A. Astashkevich and B. P. Lavrov, J. Phys. Chem. Ref. Data 44, 023105 (2015).

    ADS  Article  Google Scholar 

  34. 34.

    J. M. Hutson and P. Soldán, Int. Rev. Phys. Chem. 25, 457 (2006).

    Article  Google Scholar 

  35. 35.

    I. Georgescu, Nat. Phys. 9, 459 (2013).

    Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to S. A. Astashkevich.

Additional information

Original Russian Text © S.A. Astashkevich, 2017, published in Optika i Spektroskopiya, 2017, Vol. 122, No. 3, pp. 369–376.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Astashkevich, S.A. A systematic semiempirical study of information inequalities for the vibrational levels of a diatomic molecule for the example of the ground electronic state of 7Li2 . Opt. Spectrosc. 122, 359–365 (2017). https://doi.org/10.1134/S0030400X17020047

Download citation