Taken from Introduction to Quantum mechanics, second edition, by David Griffiths, page 47.
Solve for
Mathematica ✓
ClearAll["Global`*"]; ic = Piecewise[{{A*x*(a - x), 0 <= x <= a}, {0, True}}]; pde = I*h*D[f[x, t], t] == -((h^2*D[f[x, t], {x, 2}])/(2*m)); sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, f[x, 0] == ic}, f[x, t], {x, t}, Assumptions -> a > 0], 60*10]];
Maple ✓
restart; ic:=f(x,0)=piecewise(0<=x and x<=a,A*x*(a-x),0); pde :=I*h*diff(f(x,t),t) = -h^2/(2*m)*diff(f(x,t),x$2); cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',dsolve([pde,ic],f(x,t)) assuming a>0),output='realtime')); sol:=convert(sol,Int);
____________________________________________________________________________________