Sketch the probability density functions of electrons at

Question

1. Sketch the probability density functions of electrons at energies E₊ and E_- and k=π/a and sketch also the periodic potential V(x) using the same origin of the coordinate system.

2. Using the nearly-free electron energy band model obtained in section 181, compute the allowed energy bandwidth for a=2.35A (Si interatomic spacing) and show that 2k²k₁²/m in (181.19) is much larger than the energy gap of Si, E_G(Si)=1.2eV, by calculating its value.