Question

The effective mass m^∗ of an electron or hole in a band is defined by 

1/m^∗ = 1/ℏ² · d²E/dk² 

where k is the wave number (k = 2π/λ). For a free electron show that m^∗ = m.

Answer 1

p = kℏ   .....(1) 

E = p²/2m = k²ℏ²/2m  ....(2)