The discussion confirms that for a given wave function ##\phi(k)##, the expected values of momentum can be expressed as ##\langle p \rangle = \hbar \langle k \rangle## and ##\langle p^2 \rangle = \hbar^2 \langle k^2 \rangle##. This relationship is established based on the fundamental principles of quantum mechanics, specifically the definitions of momentum in terms of wave vector. The relevant equation provided is $$ \langle p \rangle = \int_{-\infty}^{\infty}\bar{\phi}(p,t) p \phi(p,t)dp $$, which supports the derivation of these expected values.
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Yes.Kyuubi said:Homework Statement: Just need to clarify this point.
Relevant Equations: $$ \langle p \rangle = \int_{-\infty}^{\infty}\bar{\phi}(p,t) p \phi(p,t)dp $$
Now if I'm given a ##\phi(k)##, and I'm asked to find ##\langle p \rangle##, ##\langle p^2 \rangle##, etc. Am I justified to say that ##\langle p \rangle = \hbar \langle k \rangle## and that ##\langle p^2 \rangle = \hbar^2 \langle k^2 \rangle## ?