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Expectation value of momentum

  1. Nov 8, 2014 #1


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    When calculating the expectation value of momentum of a real wavefunction is it always zero ? The momentum operator introduces an i into the integral and with real wavefunctions there is no other i to cancel and all Hermitian operators have real expectation values.
  2. jcsd
  3. Nov 8, 2014 #2


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    Staff: Mentor

    For a stationary state (e.g. any energy eigenstate of a bound system like the infinite square well), <p> must indeed be zero.

    However, for a non-stationary state, e.g. a linear combination of energy eigenstates of a bound system, in general <p> ≠ 0. Consider for example $$\Psi(x,t) = \frac{1}{\sqrt{2}} \left[ \psi_1(x)e^{-iE_1 t / \hbar} + \psi_2(x)e^{-iE_2 t / \hbar} \right]$$
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