On Sat, 14 Jun 2008, Richard Hennessy wrote:
> I have been using Griffith's "Introduction to Quantum Mechanics",
> 2nd edition. In the book there is a proof that the time independent
> Shrodinger equation can be real or complex and that it is always
> possible to find a real valued solution to this equation, so the
> complex solutions are not really necessary. The idea is that if
> there are two functions that satisfy Shrodinger's equation then even
> if they are complex you can always make them real by taking a linear
> combination of the two independent solutions.
I'd suggest slight caution. While it's true that you can construct
real solutions of Schr?dinger's equation by taking appropriate linear
combinations, I have a sort of feeling that there might be
physically-interesting boundary and far-field conditions that can be
satisfied if you have the full set of complex solutions, but not if
you limit yourself to the real solutions. If I've understood the
description of the DC Josephson effect, starting on p. 93 of
J. R. Waldram, Superconductivity of Metals and Cuprates, Institute of
Physics Publishing, Bristol, 1996, correctly, that's an example where
this matters.
I think I've reached Offtopicsville, so I'll stop now.
--
Dan