remove obsolete discussion from lecture 6

docs/lecture_6.md

@@ -93,16 +93,10 @@ Now we expand the definition of $W$:
 
 $$W = \langle \psi_+ | V(x) | \psi_- \rangle = \int_0^{a} dx \left[e^{i\pi x/a}\right]^* V(x) \left[e^{-i\pi x/a}\right] = \int_0^a e^{2\pi i x /a} V(x) = V_1$$
 
-Here $V_1$ is the first Fourier component of $V(x)$ (using a *complex* Fourier transform).
+Here $V_1$ is the first Fourier component of $V(x)$ (using a complex Fourier transform).
 
 $$ V(x) = \sum_{n=-\infty}^{\infty} V_n e^{2\pi i n x/a}$$
 
-In the book the *real symmetric* Fourier transform is used:
-
-$$ V(x) = \sum_{n=0}^{\infty} \tilde{V}_n \cos(2\pi n x/a),$$
-
-which can be used *only* when $V(x) = V(-x)$. Then the relation between the two is $\tilde{V}_n = 2 V_n$.
-
 #### Crossings between the higher bands
 
 Everything we did applies to the crossings at higher energies, only there we would get higher Fourier components of $V(x)$: $V_2$ for the crossing between the second and third band, $V_3$ for the crossing between third and 4th, etc.