Question

Quantum Mechanics

Answer 1

Solve time independent Schrodinger eqn for \[V=\frac{ a }{ \cos ^{2}kx }\]

Answer 2

My guess is that the solution will contain tan(kx), and I'm looking to see if I can corroborate this.
The graphics on this site are stopping me from typing out the time independent schroedinger equation (TISE).
\[-\frac{ h }{ 2\pi2m }\frac{ d ^{2}u }{ dx ^{2} }+\frac{ a }{ \cos ^{2}kx}u(x)=Eu(x)\]I have a copy from a book "Quantum mechanics", A.I.M Rae McGraw-Hill Book co (UK). It shows the ONE DIMENSIONAL TISE as a second order ordinary differential equation.
The potential function that you quote can be rewritten, via a trigonometric identity, as sec squared kx.
If the right hand side is put to zero, then you may have the homogeneous equation.
I think that there's a "function of a function" in there somewhere .
See how we get on ...
http://perendis.webs.com