# Energy of an electron in the conduction band (semi conductor)

First of all, I'm using the book "Introduction to Solid-State Physics, Charles Kittel, 8th edition". At page 205, he claims that the energy of an electron in the conduction band is : $$e_k = E_c + k^2 \frac{\hbar^2}{2m_e}$$

where $E_c$ is the energy in the conduction band, I simply interpreted this as if the electron had potential energy + kinetic energy. Then he says he uses the equation 6.20, that is: $$D(e)=\frac{V}{2\pi^2}*(\frac{2m}{\hbar^2})^{3/2} * e^{1/2}$$

But this equation comes from solving time-independent Schrödinger-equation without a potential, which I thought should be a part of the solution for the semiconductor. Can anyone tell me where I lost the plot?

• These two terms just use different reference points. In the first case, the valence band edge is set to 0 (which is commonly used). In the second case, the 0 point is at the conduction band edge. This is done out of convenience to simplify the terms. – engineer May 3 '18 at 5:32
• Alright, so different reference points but still solving TISE for a free electron? – John Skeet May 3 '18 at 5:38
• Yes, I would say so, but I don't have my copy of Kittel with me right now. – engineer May 3 '18 at 5:39
• thanks a lot for this answer, its been bothering me for a while now! – John Skeet May 3 '18 at 5:40