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Geometric Proof of Exact Quantization Rules in One Dimensional Quantum Mechanics

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Abstract

In terms of the construction of vector field with momentum and logarithmic derivative of wavefunction as its components, a geometric proof of an exact quantization rule in one dimensional quantum mechanics systems is given. The quantization rule arises from the SO(2) gauge transformation. In addition, the quantization rule is generalized to the case when the potential function is piecewise continuous between the two turning points.

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References

  1. Ma, Z.Q., Xu, B.W.: Quantum correction in exact quantization rules. Europhys. Lett. 69, 685 (2005)

    Article  ADS  Google Scholar 

  2. Ma, Z.Q., Xu, B.W.: Int. J. Mod. Phys. E 14, 599 (2005)

    Article  ADS  Google Scholar 

  3. Ma, Z.-Q., Xu, B.-W.: Acta Phys. Sin. 55, 1571 (2006)

    MathSciNet  Google Scholar 

  4. Wentzel, G.: Z. Phys. 38, 518 (1926)

    Article  ADS  Google Scholar 

  5. Kramers, H.A.: Z. Phys. 39, 828 (1926)

    Article  ADS  Google Scholar 

  6. Chern, X.S.: Lectures On Differential Geometry, 2nd edn., p. 160. Peking University Press, Beijing (2001) (in Chinese)

    Google Scholar 

  7. Woodhouse, N.M.J.: Geometric Quantization, vol. 218. Clarendon, Oxford (1992)

    MATH  Google Scholar 

  8. Shao, M.X., Zhu, Z.Y.: Commun. Theor. Phys. 35, 263 (2001)

    MATH  MathSciNet  Google Scholar 

  9. Shao, M.-X., Zhu, Z.-Y.: Commun. Theor. Phys. 33, 679 (2000)

    Google Scholar 

  10. Yan, L., Shao, M.X., Zhu, Z.Y.: Phys. Lett. B 419, 37 (1998)

    Article  MathSciNet  Google Scholar 

  11. Witten, E.: Nucl. Phys. B 188, 513 (1981)

    Article  ADS  Google Scholar 

  12. Cooper, F., Khare, A., Sukhatme, U.: Phys. Rep. 251, 267 (1995)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Physics Department, Henan Polytechnic University, Jiaozuo, 454000, China

    M. X. Shao & D. T. Zhang

  2. School of Physical Science and Technology, Lanzhou University, Lanzhou, 730000, China

    Y. Z. Mao

Authors
  1. M. X. Shao
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  2. Y. Z. Mao
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  3. D. T. Zhang
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Corresponding author

Correspondence to M. X. Shao.

Additional information

This work was supported by doctoral foundation of HPU.

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Shao, M.X., Mao, Y.Z. & Zhang, D.T. Geometric Proof of Exact Quantization Rules in One Dimensional Quantum Mechanics. Int J Theor Phys 48, 36–42 (2009). https://doi.org/10.1007/s10773-008-9779-x

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  • DOI: https://doi.org/10.1007/s10773-008-9779-x

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