function psi = packetfunc(v,t)
% Plots Gaussian wavepacket for given velocity and time.
% packetfunc(v,t) returns a complex vector with a Gaussian
% wavepacket with velocity v, time t, and position in
% the interval x = -10:0.01:10.  v, x, and t are dimensionless
% as described in the notes.  The magnitude squared of the
% wave function is plotted as well as its real and imaginary
% parts.

% v = 0; % dimensionless velocity
% t = 0; % dimensionless time
x = -10:0.01:10; % dimensionless position and sets range

psi = exp(i*v*(x - 0.5*v*t));
psi = psi.*exp(-0.25*((x - v*t).^2)/(1 + 0.5*i*t));
psi = psi./sqrt(1 + 0.5*i*t)/((2*pi)^0.25); 
% The convention in Matlab is to have the real part of sqrt() > 0.

plot(x,abs(psi).^2,x,real(psi),x,imag(psi))
xlabel('x')
legend('|psi |^2','real(psi)','imag(psi)')