Taken from Mathematica DSolve help pages
Solve a Schrodinger equation with potential over the whole real line.
Solve for \(f(x,t)\) \[ I f_t = - f_{xx} + 2 x^2 f(x,t) \] With boundary conditions \begin {align*} f(-\infty ,t) &= 0\\ f(\infty ,t) &=0 \end {align*}
Mathematica ✓
ClearAll["Global`*"]; pde = I*D[f[x, t], t] == -D[f[x, t], {x, 2}] + 2*x^2*f[x, t]; bc = {f[-Infinity, t] == 0, f[Infinity, t] == 0}; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, bc}, f[x, t], {x, t}], 60*10]]; sol = sol /. K[1] -> n;
\[\left \{\left \{f(x,t)\to \underset {n=0}{\overset {\infty }{\sum }}e^{-\frac {x^2+2 i (2 n+1) t}{\sqrt {2}}} c_n \text {HermiteH}\left (n,\sqrt [4]{2} x\right )\right \}\right \}\]
Maple ✗
restart; pde :=I*diff(f(x,t),t)=-diff(f(x,t),x$2)+2*x^2*f(x,t); bc:=f(-infinity ,t)=0,f(infinity,t)=0; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve([pde,bc],f(x,t))),output='realtime'));
\[f(x,t) = 0\] Trivial solution. Maple does not support \(\infty \) in boundary conditions
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