試題詳解

9. Which of the following statements are correct concerning the quantum energy eigenstate of a free particle? Let E = energy, p = momentum, and k = wave vector of the state.【複選題】
(A) E's of all eigenstates form a continuous spectrum.
(B) gives the speed of a moving wave packet formed by mixing the eigenstates with (E, p) around (E_c, P_c).
(C) A particle with k will behave approximately classically, when hitting a wall with an opening of the size L＞＞ 1/|k|.
(D) A mixed state formed of two eigenstates such as exp, where ki and k2 differ but|k₁|=| k₂|, is not an eigenstate of momentum but is that of energy.
(E) If one measures the momentum of mixed state exp(ik●r) + exp(-ik●r) for many times by performing the measurement on a very large number of identical copies of the state, the distribution of measured values will have a width of the order of |k|.