2.3.4 From Mathematica help pages

problem number 86

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*}

pict
Figure 2.19:PDE specification

Mathematica


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

Maple


\[f(x,t) = 0\] Trivial solution. Maple does not support \(\infty \) in boundary conditions

________________________________________________________________________________________