# Delta function potentials

I have a potential which is zero everywhere except at -2a , -a , 0 , a , 2a on the x-axis where there is an attractive delta potential at each of the 5 points. I know there is a maximum of 5 bound states. I know there can be no nodes for |x| > 2a and a maximum of one node between each delta potential. My question is ; why cant there be one further excited state - an antisymmetric state with a node at x=0 and 4 further nodes ; one between each delta potential ?

mfb
Mentor
What would happen with the first and second derivative of the antisymmetric wave function at x=0?

Antisymmetric wavefunction would have the form of sine so 1st derivative would be cos(0) =1 , 2nd derivative would be sin(0)=0. I can't see how that helps and the same would happen for the 1st and 3rd excited states as well

Staff Emeritus
I suggest you sketch the wavefunctions. If you encounter difficulty, sketch the wavefunctions for one delta potential, then two, then three, etc.

I tried that. I can manage to draw an antisymmetric wavefunction that goes through x=0 and has 4 other nodes !

Avodyne