In an interesting version of the energy-time uncertainty principle31 Δt = τ/π, where τ is the time it takes Ψ(x, t) to evolve into a state orthogonal to Ψ(x,0). Test this out, using a wave function that is an equal admixture of two (orthonormal) stationary states of some (arbitrary) potential: Ψ(x, 0) = (1/√2)[ψ1(x)+ψ2(x)].
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