The absorption and rotation of light is derived for a free electron constrained to move on a helix. This model is probably the simplest optically active system for which exact wavefunctions can be obtained. It is found that a randomly oriented right‐handed helix has a positive rotational strength for the longest wavelength absorption band. As expected, this free electron model gives results very similar to an exciton model in which only nearest‐neighbor interactions are considered.
REFERENCES
1.
2.
L. I. Schiff, Quantum Mechanics (McGraw‐Hill Book Company, Inc., New York, 1955), p. 249.
3.
4.
5.
A.
Moscowitz
, Advan. Chem. Phys.
4
, 67
(1962
).6.
7.
8.
As the helix becomes large compared to the wavelength of light, neither the absorption nor the optical rotation can be accurately characterized by the electric and magnetic transition dipole moments. Instead the transition probability integral2 should be used. Therefore we should assume that the wavelength of the incident beam is also becoming very large.
9.
For the infinite helix so we can refer to perpendicular incidence without specifying the direction further as being along x or y. This is not true for a finite helix.
10.
11.
A. Moscowitz, Ph.D. thesis, Harvard University, 1957.
12.
13.
14.
W.
Moffitt
, D. D.
Fitts
, and J. G.
Kirkwood
, Proc. Natl. Acad. Sci. (U.S.)
43
, 723
(1957
).15.
16.
17.
Further details can be found in the Ph.D. thesis (University of California, Berkeley, 1962) of R. W. Woody.
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© 1964 American Institute of Physics.
1964
American Institute of Physics
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