(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

In an infinite potential hole, the ground state is described by the wavefunction ψ=A*sin([itex]\frac{πx}{a}[/itex]). Does the ground state have a definite momentum? If not, then what are the values of momentum in ground state?

2. Relevant equations

Wavefunction ψ=A*sin([itex]\frac{πx}{a}[/itex])

Momentum operator [itex]\hat{p}[/itex]=-iħ[itex]\frac{d}{dx}[/itex]

3. The attempt at a solution

Momentum has a definite value when [itex]\hat{p}[/itex]ψ=pψ.

In this case [itex]\frac{dψ}{dx}[/itex]=[itex]\frac{π}{a}[/itex]A*cos([itex]\frac{πx}{a}[/itex])

and [itex]\hat{p}[/itex]ψ=-[itex]\frac{iħπA}{a}[/itex]*cos([itex]\frac{πx}{a}[/itex])

So this is the point where I am stuck, what does this result show me?

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# Homework Help: Momentum values in quantum mechanics

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