3.1.6 From Mathematica help pages

problem number 148

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*}

Figure 3.5: PDE specification

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;
 

\[\left \{\left \{f(x,t)\to \sum _{n=0}^\infty e^{-\frac {x^2+2 i (2 n+1) t}{\sqrt {2}}} c_n \operatorname {HermiteH}\left (n,\sqrt [4]{2} x\right )\right \}\right \}\]

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