Expansion in energy eigenstates

Expansion in energy eigenfunctions

Simulation

Expansion Game

Superposition $u (x)$

Use the controls to choose a spatial quantum wave function $u (x)$ at time $t = 0$ of a quantum particle in an infinite square well, and to show its decomposition into energy eigenfunctions. Press the ? buttons for more information.

Can you predict which expansion coefficients (if any) will be zero for a give $u (x)$ , which coefficient will have the largest amplitude and its sign? Then try the expansion game to test your knowledge!

Main controls

Superposition $u (x)$ at time $t = 0$ :

$N \sin^{5} (\frac{π x}{L})$

Show expansion in energy eigenfunctions

Overlay eigenfunctions in

u (x)

graph

$u (x)$ =

$c_{1} u_{1} (x)$

$c_{1} \approx 0.89$

$c_{3} u_{3} (x)$

$c_{3} \approx - 0.45$

$c_{2} = c_{4} = c_{6} = \dots = 0$

+...

$c_{5} u_{5} (x)$

$c_{5} \approx 0.09$

$u (x)$ and $\sum_{n} c_{n} u_{n} (x)$

individual $c_{n} u_{n} (x)$

Your score:

0/100

Match the coefficients for the first six terms of the expansion for $u (x)$ as closely as possible using the sliders below, or the arrows for more fine control. Coefficients that should be zero must be set to zero exactly!