2.3.1 Logan textbook, page 30

problem number 83

From page 30, David J Logan textbook, applied PDE textbook.

Schrodinger PDE with zero potential (Logan p. 30)

Solve \[ I \hbar f_t = - \frac {\hbar ^2}{2 m} f_{xx} \] With boundary conditions \begin {align*} f(0,t) &= 0\\ f(L,0) &=0 \end {align*}

pict
Figure 2.16:PDE specification

Mathematica


\[\left \{\left \{f(x,t)\to \underset {n=1}{\overset {\infty }{\sum }}e^{-\frac {i h n^2 \pi ^2 t}{2 L^2 m}} c_n \sin \left (\frac {n \pi x}{L}\right )\right \}\right \}\]

Maple


\[f \left (x , t\right ) = \Mapleoverset {\infty }{\Mapleunderset {n =1}{\sum }}\mathit {\_F1} (n ) {\mathrm e}^{-\frac {i \pi ^{2} h n^{2} t}{2 L^{2} m}} \sin \left (\frac {\pi n x}{L}\right )\]

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