In an interesting version of the energy-time uncertainty principle t = /, where is the time

In an interesting version of the energy-time uncertainty principle 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 a linear combination of two (orthonormal) stationary states of some (arbitrary) potential:

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¥ (x, 0) = (1/√2) [v1 (x) +¥2(x)].