Given a differential equation
(1) |
(2) |
(3) |
(4) |
(5) |
(6) | |||
(7) |
A nonself-adjoint second-order linear differential operator can always be transformed into a self-adjoint one using
Sturm-Liouville Theory. In the special case , (7) gives
(8) |
(9) |
(10) |
(11) |
A self-adjoint operator which satisfies the Boundary Conditions
(12) |
See also Adjoint Operator, Hermitian Operator, Sturm-Liouville Theory
References
Arfken, G. ``Self-Adjoint Differential Equations.'' §9.1 in Mathematical Methods for Physicists, 3rd ed.
Orlando, FL: Academic Press, pp. 497-509, 1985.
© 1996-9 Eric W. Weisstein