Selection rules for processes involving photon-molecule interaction A symmetry-conservation-based approach bypassing transition matrix elements

Journal of Chemical Education

Volumn 73, Issue 8, 1996, Pages 743-746

  Chowdhury, Mihir ^a  

^a DEPARTMENT OF MATERIALS SCIENCE   (India)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040922759     PISSN: 00219584     EISSN: None     Source Type: Journal    
DOI: 10.1021/ed073p743     Document Type: Article

References (12)

1. For example, the symmetry of physical laws with respect to time displacement leads to energy conservation. Symmetries with respect to linear and angular displacement in space are responsible for momentum and angular-momentum conservation, whereas equivalence of right-handed and left-handed systems (not true for nuclear β-decay though) leads to parity conservation. For a lucid discussion of the conservation principles, see (a) Feynmann, R. P.; Leighton, R. B.; Sands The Feynmann Lectures on Physics; Narosa (Indian Standard Edition, 1990); Vol. 1, Chapter 52. (b) Bransden, B. H.; Joachain, C. J. Introduction to Quantum Mechanics; English Language Book Society: Longman, U.K., 1990; pp 232-242. For a comprehensive critical discussion, see (c) Stedman, G. E. Am. J. Phys. 1983, 51, 753.
2. For example, the symmetry of physical laws with respect to time displacement leads to energy conservation. Symmetries with respect to linear and angular displacement in space are responsible for momentum and angular-momentum conservation, whereas equivalence of right-handed and left-handed systems (not true for nuclear β-decay though) leads to parity conservation. For a lucid discussion of the conservation principles, see (a) Feynmann, R. P.; Leighton, R. B.; Sands The Feynmann Lectures on Physics; Narosa (Indian Standard Edition, 1990); Vol. 1, Chapter 52. (b) Bransden, B. H.; Joachain, C. J. Introduction to Quantum Mechanics; English Language Book Society: Longman, U.K., 1990; pp 232-242. For a comprehensive critical discussion, see (c) Stedman, G. E. Am. J. Phys. 1983, 51, 753.
3. For example, the symmetry of physical laws with respect to time displacement leads to energy conservation. Symmetries with respect to linear and angular displacement in space are responsible for momentum and angular-momentum conservation, whereas equivalence of right-handed and left-handed systems (not true for nuclear β-decay though) leads to parity conservation. For a lucid discussion of the conservation principles, see (a) Feynmann, R. P.; Leighton, R. B.; Sands The Feynmann Lectures on Physics; Narosa (Indian Standard Edition, 1990); Vol. 1, Chapter 52. (b) Bransden, B. H.; Joachain, C. J. Introduction to Quantum Mechanics; English Language Book Society: Longman, U.K., 1990; pp 232-242. For a comprehensive critical discussion, see (c) Stedman, G. E. Am. J. Phys. 1983, 51, 753.
4. The justification of this simple principle is as follows. The total Hamiltonian for the combined photon-molecule system consists of a molecular part, a photon part and a term representing the interaction between the two. The last term is assumed to be invariant under all possible rotation-inversion operations. Hence the total Hamiltonian is invariant under all the spatial symmetry operations for which the Hamiltonian of the molecule as well as that of the photon remains unchanged These symmetry elements should therefore be constants of motion (i.e their symmetry characteristics should be preserved).
5. A detailed discussion of all nonlinear processes is given in Yariv, A. Quantum Electronics; John Wiley and Sons: NY, 1989; pp 64, 378, 392.
6. The matrix elements for optical activity or circular dichroism was discussed in Eyring, H.; Walter, J.; Kimball, G. E. Quantum Chemistry. An enlightening discussion of symmetry elements appropriate for optical activity is given in Barron, L. D. Chem. Soc. Rev. 1986, 15, 189. See also Mason, S. F. Molecular Optical Activity and the Chiral Discriminations; Cambridge University: Cambridge, 1982, and Chowdhury, M.; Karmakar, B. In Rare Earth Spectroscopy; Jezowska-Trzebiatowska, B.; Legendziewicz, J.; Strek, W., Eds.; World Scientific, 1985; p 114.
7. The matrix elements for optical activity or circular dichroism was discussed in Eyring, H.; Walter, J.; Kimball, G. E. Quantum Chemistry. An enlightening discussion of symmetry elements appropriate for optical activity is given in Barron, L. D. Chem. Soc. Rev. 1986, 15, 189. See also Mason, S. F. Molecular Optical Activity and the Chiral Discriminations; Cambridge University: Cambridge, 1982, and Chowdhury, M.; Karmakar, B. In Rare Earth Spectroscopy; Jezowska-Trzebiatowska, B.; Legendziewicz, J.; Strek, W., Eds.; World Scientific, 1985; p 114.
8. The matrix elements for optical activity or circular dichroism was discussed in Eyring, H.; Walter, J.; Kimball, G. E. Quantum Chemistry. An enlightening discussion of symmetry elements appropriate for optical activity is given in Barron, L. D. Chem. Soc. Rev. 1986, 15, 189. See also Mason, S. F. Molecular Optical Activity and the Chiral Discriminations; Cambridge University: Cambridge, 1982, and Chowdhury, M.; Karmakar, B. In Rare Earth Spectroscopy; Jezowska-Trzebiatowska, B.; Legendziewicz, J.; Strek, W., Eds.; World Scientific, 1985; p 114.
9. The matrix elements for optical activity or circular dichroism was discussed in Eyring, H.; Walter, J.; Kimball, G. E. Quantum Chemistry. An enlightening discussion of symmetry elements appropriate for optical activity is given in Barron, L. D. Chem. Soc. Rev. 1986, 15, 189. See also Mason, S. F. Molecular Optical Activity and the Chiral Discriminations; Cambridge University: Cambridge, 1982, and Chowdhury, M.; Karmakar, B. In Rare Earth Spectroscopy; Jezowska-Trzebiatowska, B.; Legendziewicz, J.; Strek, W., Eds.; World Scientific, 1985; p 114.
10. A lucid discussion of angular momentum of light quanta is given in some of the early papers of C. V. Raman. See Scientific papers of C. V. Raman; Ramasheshan, S., Eds.; Indian Academy of Sciences: Bangalore, India, 1988; Vol. 1, pp 481-496. See also Oppenheimer, J. R. Physical Review 1931, 38, 726 and ref 1c.
11. A lucid discussion of angular momentum of light quanta is given in some of the early papers of C. V. Raman. See Scientific papers of C. V. Raman; Ramasheshan, S., Eds.; Indian Academy of Sciences: Bangalore, India, 1988; Vol. 1, pp 481-496. See also Oppenheimer, J. R. Physical Review 1931, 38, 726 and ref 1c.
12. For discussion of symmetry-based Woodward-Hoffman type selection rules for chemical reactions, see Cotton, F. A. Chemical Applications of Group Theory; Wiley Eastern, 1989.