We present an alternative approach to the teaching of introductory quantum mechanics by considering the interaction between a particle and a waveguide. We focus on the accumulated phase when the particle travels across a waveguide composed of an arbitrary number of rectangular sections and show that the condition for resonant transmission can be deduced to leading order by simple algebra.
REFERENCES
1.
H. D.
Young
and R. A.
Freedman
, University Physics with Modern Physics
(Addison-Wesley
, New York
, 2008
).2.
M.
Alonso
and E. J.
Finn
, Fundamental University Physics-Quantum and Statistical Physics
(Addison-Wesley
, London
, 1983
).3.
A. P.
French
and E. F.
Taylor
, An Introduction to Quantum Physics
(W.W. Norton & Company
, New York
, 1978
).4.
5.
S.
Weinberg
, The Quantum Theory of Fields
(Cambridge U. P.
, Cambridge, UK
, 1995
).6.
J. -M.
Lévy-Leblond
, “A geometrical quantum phase effect
,” Phys. Lett. A
125
, 441
–442
(1987
).7.
R. E.
Kastner
, “Geometrical quantum phase effect and Bohm’s quantum potential
,” Am. J. Phys.
61
, 852
–852
(1993
).8.
9.
F. J.
Garcia-Vidal
, L.
Martin-Moreno
, T. W.
Ebbesen
, and L.
Kuipers
, “Light passing through subwavelength apertures
,” Rev. Mod. Phys.
82
, 729
–787
(2010
).© 2011 American Association of Physics Teachers.
2011
American Association of Physics Teachers
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.
