Appendix F: The Harmonic Oscillator
235
and
χ n |q| χ n =
1
√
2
χ n
ˆ
a + ˆ
a
†
χ n
=
n + 1
2
δ n+1,n +
n
2
δ n−1,n .
(F.15)
References
1. Heller, E.J.: Time–dependent approach to semiclassical dynamics. J. Chem. Phys.
62, 1544–1555 (1975)
2. Heller, E.J.: The semiclassical way to molecular spectroscopy Acc. Chem. Res.
14, 368–375 (1981)
3. Tannor, D.J., Heller, E.J.: Polyatomic Raman scattering for general harmonic
potentials. J. Chem. Phys. 77, 202–218 (1982)
4. Heller, E.J., Sundberg, R.L., Tannor, D.: Simple aspects of Raman scattering. J.
Phys. Chem. 86, 1822–1833 (1982)
5. Tannor, D.J.: Introduction to Quantum Mechanics: A Time-dependent Perspective. University Science Books, Sausalito (2007)
6. Merzbacher, E.: Quantum Mechanics. Wiley, New York (1998)
235
and
χ n |q| χ n =
1
√
2
χ n
ˆ
a + ˆ
a
†
χ n
=
n + 1
2
δ n+1,n +
n
2
δ n−1,n .
(F.15)
References
1. Heller, E.J.: Time–dependent approach to semiclassical dynamics. J. Chem. Phys.
62, 1544–1555 (1975)
2. Heller, E.J.: The semiclassical way to molecular spectroscopy Acc. Chem. Res.
14, 368–375 (1981)
3. Tannor, D.J., Heller, E.J.: Polyatomic Raman scattering for general harmonic
potentials. J. Chem. Phys. 77, 202–218 (1982)
4. Heller, E.J., Sundberg, R.L., Tannor, D.: Simple aspects of Raman scattering. J.
Phys. Chem. 86, 1822–1833 (1982)
5. Tannor, D.J.: Introduction to Quantum Mechanics: A Time-dependent Perspective. University Science Books, Sausalito (2007)
6. Merzbacher, E.: Quantum Mechanics. Wiley, New York (1998)