Show that the wave function for a particle in the periodic delta function potential can be written in the form ψ ( x ) = C { sin ( k x ) + e − i q a sin [ k ( a − x ) ] } , ( 0 ≤ x ≤ a ) .

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Chapter 5.3, Problem 5.24P

(a)

To determine

Show that the wave function for a particle in the periodic delta function potential can be written in the form ψ(x)=C{sin(kx)+e−iqasin[k(a−x)]}, (0≤x≤a).

(b)

To determine

The correct wave function for the case at the top of a band yields ψ(x)=0/0.

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