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## Main Question or Discussion Point

Question 1: If we consider that each atom in a cristal solid is a harmonic oscillator with the energy eigenvalues [tex](n+1/2) \hbar \omega[/tex] and if one oscillator has for example an energy [tex](1+1/2) \hbar \omega[/tex], does this mean that there is a phonon located on this atom?

Question 2: If this is true, can we define a wave function, [tex]\psi (x)[/tex] for example, as the sum (or the integral) of plane waves that describes the amplutide of finding the phonon somewhere on the [tex]x[/tex] axis?

Question 3: Does a single phonon in a solid cristal behave in the same manner as a free electron in a box for exemple?

Thank you.

Question 2: If this is true, can we define a wave function, [tex]\psi (x)[/tex] for example, as the sum (or the integral) of plane waves that describes the amplutide of finding the phonon somewhere on the [tex]x[/tex] axis?

Question 3: Does a single phonon in a solid cristal behave in the same manner as a free electron in a box for exemple?

Thank you.