TEST 5 ( 2/12/23)
A quantum particle of mass m moves in the potential V(x).
(a) Write the time dependent Schrodinger Equation [2]
(b) Suppose the initial wave function is
 ( x,0) 
1
2 (x) 
2 0.25

( x  x0 ) 2 
,
Exp ikx 
4(x) 2 

calculate the Fourier
transform of the above initial wave function
[5]
(c) Write the ( x.t ) in terms of (x,0) using pseudo spectral
method ( show all the steps) [8]
(d) Optional: Solve numerically with suitable data from the
textbook [0] (bonus marks =15)