By taking into account that the equations of motion of classical mechanics can be expressed in terms of differential operators in phase space, we develop a simple method for obtaining exact solutions for several models in one and more dimensions. We also propose a simple procedure for the systematic construction of exactly solvable models in one dimension.
REFERENCES
1.
H. Goldstein, Classical Mechanics, 2nd ed. (Addison-Wesley, Reading, MA, 1980).
2.
C. F.
de Souza
and M. M.
Gandelman
, “An algebraic approach for solving mechanical problems
,” Am. J. Phys.
58
, 492
–495
(1990
).3.
F. M. Fernández, Introduction to Perturbation Theory in Quantum Mechanics (CRC, Boca Raton, FL, 2000).
4.
D.
Rapp
and T.
Kassal
, “The theory of vibrational energy transfer between simple molecules in nonreactive collisions
,” Chem. Rev.
69
, 61
–102
(1969
).5.
Maple 7, Waterloo Maple, Inc., 2000.
This content is only available via PDF.
© 2002 American Association of Physics Teachers.
2002
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.