7. Write the expressions for momentum vector (k), wave function Y (x) and energy of electrons that are free to move between atoms and are experiencing no potential field (V(x) =0).

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7. Write the expressions for momentum vector (k), wave function Y (x) and energy of electrons
that are free to move between atoms and are experiencing no potential field (V(x) =0).
Transcribed Image Text:7. Write the expressions for momentum vector (k), wave function Y (x) and energy of electrons that are free to move between atoms and are experiencing no potential field (V(x) =0).
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Step 1

The expression for momentum vector, wave function and energy is to be evaluated.

-h28π2md2ψdx2+V(x) ψ(x)=Eψ(x)V(x)=0-h28π2md2ψdx2+0=Eψ(x)-h28π2md2ψdx2=Eψd2ψdx2=-8π2mEψh2d2ψdx2+8π2mEψh2=0d2ψdx2+k2ψ=0    (1)k=8π2mEh2

 

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