Superpositions in Time: 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,t) = (1/2)^-1/2 [f_n1 (x,t) + f_n2 (x,t)]

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or

Y_n1n2(x,t) = (1/2)^-1/2 [ sin(n₁px)*e(2pi n₁² E₁t/h) + sin(n₂px)*e(2pi n₂² E₁t/h)]

therefore

Y*Y = (1/2) [ sin²(n₁px) +sin²(n₂px) +2*sin(n₁px)*sin(n₂px)*cos(2p(n₁² - n₂²)E₁t/h) ]