In Reply to: Assignment 6 #6a posted by Brian on March 09, 2004 at 01:00:39:
>For the Schrodinger equation problem, we are asked to derive the FT for psi. From Thm 1.3 in Chapter 5, if f is Schwartz, then the FT of f must be Schwartz. However, in problem 6a, the given FT of psi is definitely not Schwartz (increases exponentially) even though psi is Schwartz for each t. Is there a minus sign missing in the exponent? Likewise, is the formula for psi (using the Fourier inversion formula) correct? It seems the minus sign in the second exponential term is misplaced.
Oops! The minus signs are indeed in the wrong place; in the formula
for psi(x,t), the first exponential should have a minus sign
and the second should not (instead of the other way around).
The FT still doesn't increase exponentially though, because
of the presence of the i in the exponent.
Terry