Why are these molecular orbitals invalid for hexatriene? Here are the MOs (more accurately, the breakdown of the MOs) for conjugated hexatriene:



Now, when first asked to draw the MOs myself, I drew this one for $\psi_3$:



It still has two nodes, and is still symmetric. I see nothing wrong with it, except that it doesn't match the "correct" MOs. 

Similarly, for $\psi^*_4$, I can draw





Now, as I understand it, MOs are formed from various combinations of atomic orbitals, subject to a few rules regarding symmetry. From what I know, the two MOs I've given above should be valid MOs for hexatriene, or at least components of an MO of hexatriene. 

Why aren't these two MOs valid? Also, is there a methodical way to obtain the sequence of MOs in the general case(of a conjugated polyene)?
I read up a bit about Huckel theory. There's a pdf that explains this particularly well.

At one point, the following formula is derived at one point:

$$c_s\propto\sin\left(\frac{\pi k s}{n+1}\right)$$

which gives the coefficient (sans a positive normalisation constant) of the atomic orbital of the $s$th atom in the $k$th MO of a conjugated linear or monocyclic system on $n$ atoms.

A quick and dirty method has also been provided.



Using this, one can get a general idea of how the MO should look, and then one can get the exact +/- sequence by considering the number of nodes. Note that this is really the same thing as applying the $c_s$ formula given above, just in a graphical manner.