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The rotating harmonic oscillator revisited

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Abstract

We analyze the distribution of the eigenvalues of the quantum-mechanical rotating harmonic oscillator by means of the Frobenius method. A suitable ansatz leads to a three-term recurrence relation for the expansion coefficients. Truncation of the series yields some particular eigenvalues and eigenfunctions in exact analytical form. The former can be organized in such a way that one obtains suitable information about the whole spectrum of the model.

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References

  1. R.E. Langer, Phys. Rev. 75, 792 (1949)

    Article  CAS  Google Scholar 

  2. N. Fröman, P.O. Fröman, Ann. Phys. 115, 269 (1978)

    Article  Google Scholar 

  3. G.P. Flessas, Phys. Lett. A 71, 315 (1979)

    Article  Google Scholar 

  4. N. Fröman, P.O. Fröman, F. Karlsson, Phys. Lett. A 77, 397 (1980)

    Article  Google Scholar 

  5. G.P. Flessas, Nuovo Cimento B 64, 358 (1981)

    Article  Google Scholar 

  6. F. Karlsson, P.O. Fröman, A. Hökback, Nuovo Cimento B 70, 155 (1982)

    Article  Google Scholar 

  7. V. Singh, S.N. Biswas, K. Datta, J. Math. Phys. 23, 1323 (1982)

    Article  CAS  Google Scholar 

  8. M.M. Nieto, V.P. Gutschick, Phys. Rev. A 28, 471 (1983)

    Article  CAS  Google Scholar 

  9. D. Masson, J. Math. Phys. 24, 2074 (1983)

    Article  Google Scholar 

  10. D. Masson, J. Math. Phys. 24, 2089 (1983)

    Article  Google Scholar 

  11. R.S. Gangopadhyay, G. Ghosh, B. Dutta-Roy, Phys. Rev. A 30, 594 (1984)

    Article  CAS  Google Scholar 

  12. B. Leaute, G. Marcilhacy, J. Phys. A 19, 3527 (1986)

    Article  Google Scholar 

  13. J. Killingbeck, J. Phys. A 20, 1285 (1987)

    Article  CAS  Google Scholar 

  14. R. Roychoudhury, Y.P. Varshni, Phys. Rev. A 37, 2309 (1988)

    Article  CAS  Google Scholar 

  15. W. Lay, S. Slavyanov, A. Smirnov, Phys. Lett. A 172, 305 (1993)

    Article  Google Scholar 

  16. F.M. Fernández, Dimensionless equations in non-relativistic quantum mechanics. arXiv:2005.05377 [quant-ph]

  17. P. Güttinger, Z. Phys. 73, 169 (1932)

    Article  Google Scholar 

  18. R.P. Feynman, Phys. Rev. 56, 340 (1939)

    Article  CAS  Google Scholar 

  19. M.S. Child, S.-H. Dong, X.-G. Wang, J. Phys. A 33, 5653 (2000)

    Article  Google Scholar 

  20. P. Amore, F.M. Fernández, Phys. Scr. 95, 105201 (2020). arXiv:2007.03448 [quant-ph]

    Article  CAS  Google Scholar 

Download references

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  1. INIFTA, División Química Teórica, Blvd. 113 y 64 (S/N), Sucursal 4, Casilla de Correo 16, 1900, La Plata, Argentina

    Francisco M. Fernández

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  1. Francisco M. Fernández
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Correspondence to Francisco M. Fernández.

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Fernández, F.M. The rotating harmonic oscillator revisited. J Math Chem 60, 555–561 (2022). https://doi.org/10.1007/s10910-021-01320-9

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  • DOI: https://doi.org/10.1007/s10910-021-01320-9

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