Mathematics · Quantum Mechanics

Consider a particle in a symmetric one-dimensional infinite square well potential V(x) = 0 for |x| ≤ L/2 and ∞ for |x| > L/2. At time t = 0, the particle is in an equal superposition state ψ(x, 0) = 1√2(φ1(x) + φ2(x)), where φ1(x) and φ2(x) are normalized ground and first excited states. If τ is the minimum time at which the particle is equally likely to be found in either half of the well, calculate the value of τ hm L2 where h is Planck's constant and m is mass.