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Consider a particle in an infinite square well described initially by a wave that is superposition of the ground state and the first excited states of the well: Ψ(x,t = 0) = C[ψ1(x) +ψ 2 (x)]
(a) show that the value C =1/ 2 normalizes this wave, assuming 1 ψ and 2 ψ are themselves normalized.
(b)find Ψ(x,t) at any later time t.
(c) show that the superposition state is not a stationary state, but that the average energy of this state is the arithmetic mean (E1+E2)/2 of the ground state energy E1 and the first excited state energy E2.
(a) show that the value C =1/ 2 normalizes this wave, assuming 1 ψ and 2 ψ are themselves normalized.
(b)find Ψ(x,t) at any later time t.
(c) show that the superposition state is not a stationary state, but that the average energy of this state is the arithmetic mean (E1+E2)/2 of the ground state energy E1 and the first excited state energy E2.
