Time-dependent Superpositions and Expectation Values: Infinite Square Well 

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The superposition shown is an equal mix of the two states n₁ and n₂ for the infinite square well, Y_n1n2(x)=(1/2)^-1/2 [f_n1 (x) + f_n2 (x)].

The integral over the length of the well calculates <x> for the given time-dependent wavefunction.

Note that the value of <x> varies about 0.5 (the middle of the well) to give values of <x> from about 0.32 to 0.68 for n₁=1 and n₂=2!