Bulletin of the Korean Chemical Society

Korean Chemical Society (대한화학회)
권호 표지
DOI QR코드

DOI QR Code

Observation of Supersymmetry in Rigid Symmetric Top Rotor

  • Sun, Ho-Sung (Department of Chemistry, Sungkyunkwan University)
  • Published : 2006.04.20
Download PDF
⟨ Previous Next ⟩

Abstract

It is explicitly shown that a supersymmetry structure exists in the spectrum of a rigid symmetric top rotor in the molecule-fixed frame. Using projection operators constructed from the time-reversal symmetry of the rotor, the full rotor Hamiltonian is separated into two parts, i.e., the bosonic and fermionic components. The construction, without ambiguity, suggests that the rotor has a supersymmetry in it. This supersymmetry is mathematically equivalent to that of the free rotor on a plane recently noted by Rau.

Keywords

References

  1. Miller, D. Nature 1997, 385, 768 https://doi.org/10.1038/385768a0
  2. Witten, E. Nature 2004, 429, 507 https://doi.org/10.1038/429507a
  3. Cooper, F.; Khare, A.; Sukhatme, U. P. Supersymmetry in Quantum Mechanics; World Scientific: Singapore, 2001
  4. Iachello, F. Phys. Rev. Lett. 1980, 44, 772 https://doi.org/10.1103/PhysRevLett.44.772
  5. Balantekin, A. B.; Bars, I.; Iachello, F. Phys. Rev. Lett. 1981, 47, 19 https://doi.org/10.1103/PhysRevLett.47.19
  6. Sourlas, N. Physica D 1985, 15, 115 https://doi.org/10.1016/0167-2789(85)90153-8
  7. Cardy, J. L. Physica D 1985, 15, 123 https://doi.org/10.1016/0167-2789(85)90154-X
  8. Tangerman, R. D.; Tjon, J. A. Phys. Rev. A 1993, 48, 1089 https://doi.org/10.1103/PhysRevA.48.1089
  9. Kostelecky, V. A.; Nieto, M. M. Phys. Rev. Lett. 1984, 53, 2285 https://doi.org/10.1103/PhysRevLett.53.2285
  10. Rau, A. R. P. Phys. Rev. Lett. 1986, 56, 95 https://doi.org/10.1103/PhysRevLett.56.95
  11. Kostelecky, V. A.; Nieto, M. M. Phys. Rev. Lett. 1986, 56, 96 https://doi.org/10.1103/PhysRevLett.56.96
  12. Kostelecky, V. A.; Nieto, M. M. Phys. Rev. A 1985, 32, 1293
  13. Kostelecky, V. A.; Nieto, M. M. Phys. Rev. A 1985, 32, 3243
  14. Bluhm, R.; Kostelecky, V. A. Phys. Rev. A 1993, 47, 794 https://doi.org/10.1103/PhysRevA.47.794
  15. Bluhm, R.; Kostelecky, V. A. Phys. Rev. A 1994, 49, 4628 https://doi.org/10.1103/PhysRevA.49.4628
  16. Sukumar, C. V. J. Phys. A: Math. Gen. 1985, 18, L697 https://doi.org/10.1088/0305-4470/18/12/002
  17. Jarvis, P. D.; Stedman, G. E. J. Phys. A: Math. Gen. 1986, 19, 1373 https://doi.org/10.1088/0305-4470/19/8/019
  18. Haymaker, R. W.; Rau, A. R. P. Am. J. Phys. 1986, 54, 928 https://doi.org/10.1119/1.14794
  19. Lahiri, A.; Roy, P. K.; Bagchi, B. Int. J. Mod. Phys. 1990, 5, 1383 https://doi.org/10.1142/S0217751X90000647
  20. Wigner, E. P. Group Theory; Academic Press: New York, 1959
  21. Tinkham, M. Group Theory and Quantum Mechanics; McGraw-Hill: New York, 1964
  22. Bunker, P. R. Molecular Symmetry and Spectroscopy; Academic Press: New York, 1979
  23. Zare, R. N. Angular Momentum; Wiley: New York, 1988
  24. Rau, A. R. P. J. Phys. A: Math. Gen. 2004, 37, 10421 https://doi.org/10.1088/0305-4470/37/43/028
  25. Nikitin, A.; Champion, J. P. J. Mol. Spectrosc. 2005, 230, 168 https://doi.org/10.1016/j.jms.2004.10.012
  26. Cooper, F.; Kahre, A.; Sukhatme, U. P. Phys. Rep. 1995, 251, 267 https://doi.org/10.1016/0370-1573(94)00080-M
  27. Cumbescure, M.; Gieres, F.; Kibler, M. J. Phys. A: Math. Gen. 2004, 37, 10385 https://doi.org/10.1088/0305-4470/37/43/025
  28. Plyushchay, M. S. Ann. Phys. 1996, 245, 339 https://doi.org/10.1006/aphy.1996.0012
  29. Plyushchay, M. S. Nucl. Phys. B 1999, 543, 447 https://doi.org/10.1016/S0550-3213(98)00832-3
  30. Sun, H. Bull. Korean Chem. Soc. 2005, 26, 1717 https://doi.org/10.1007/s11814-009-0235-2

Cited by

  1. The Analytical Transfer Matrix Method Combined with Supersymmetry: Coulomb Potential vol.28, pp.3, 2006, https://doi.org/10.5012/bkcs.2007.28.3.408
  2. Eigenenergies of 3D-Coulomb and 3D-Harmonic Oscillator Potentials from WKB Quantization: Point Canonical Transformation vol.29, pp.1, 2006, https://doi.org/10.5012/bkcs.2008.29.1.085
  3. Physical Chemistry Research Articles Published in the Bulletin of the Korean Chemical Society: 2003-2007 vol.29, pp.2, 2008, https://doi.org/10.5012/bkcs.2008.29.2.450
  4. On the Size of Quantum Dots with Bound Hydrogenic Impurity States vol.30, pp.2, 2006, https://doi.org/10.5012/bkcs.2009.30.2.315