Expansion in energy eigenfunctions
Simulation
Expansion Game
Superposition \(u(x)\)
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Main controls
Superposition \(u(x)\) at time \(t=0\):
N sin5(pi x/L)
\(u(x)\) =
+
c1u1(x)
c1 ≈ 0.89
+
c3u3(x)
c3 ≈ −0.45
c2 = c4 = c6 = ... = 0
+...
c5u5(x)
c5 ≈ 0.09
\(u(x)\) and \(\sum_n c_{n \,} u_n(x)\)
individual \(c_{n \,} u_n(x)\)
c1 = 0.00
c2 = 0.00
c3 = 0.00
c4 = 0.00
c5 = 0.00
c6 = 0.00