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My book states the following, "when a particle, in a stationary state, is bound the expectation value of its momentum is zero" but it never elaborates why.

I know that $$\int\Psi^*(x,t)\hat{Q}\Psi(x,t)dx$$

but why would that necessarily mean that the expectation value of its momentum is zero?

Robben
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  • Answered already : https://physics.stackexchange.com/questions/100277/expectation-of-momentum-in-the-bound-state Scroll through the answers and you'll find multiple good approaches – Andrew Apr 25 '20 at 06:48
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    Does this answer your question? Expectation of momentum in the bound state –  Apr 25 '20 at 06:54
  • Have you tried actually finding the wavefunction for a bound state or calculating its $\langle \hat p \rangle$ ? You'll find the particle spends an equal amount of time in the $+x$ and $-x$ sections of the well. Additionally, this is explicitly addressed here from a simple google search... https://chem.libretexts.org/Courses/Pacific_Union_College/Quantum_Chemistry/03%3A_The_Schr%C3%B6dinger_Equation_and_a_Particle_in_a_Box/3.07%3A_The_Average_Momentum_of_a_Particle_in_a_Box_is_Zero – Andrew Apr 25 '20 at 07:03

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