# Questions on the defination of wave number and propagation constant in energy gaps

1. Sep 3, 2006

### jasum

Hi, I just get confused on the some definations in the energy gap theory.

in the equation
$$\cos {k_1a} \cos{k_2b} - \frac{k_1^2 + k_2^2}{2k_1k_2} \sin {k_1a} \sin{k_2b} = \cos {kd}$$
where
$$\frac {\hbar ^2 k_1^2}{2m} = E$$
$$\frac {\hbar ^2 k_2^2}{2m} = E - V$$

however the eigenergies
$$\frac {\hbar ^2 k^2}{2m} = E$$

Here I just get confused
what is the physical meaning of k1,k2 and k?
and what is the difference of the energy calculated from k and k_1?

Last edited: Sep 3, 2006