# Inhomogenous Schrödinger equation

Please help me out in solving this inhomogeneous Schrödinger equation in cylindrical co-ordinates [You may suggest if I have to go for mathematics]:

$$\ddot R + \frac1r\dot R+\left(b^2-d^2-\frac{a^2}{r^2}\right) R - \frac{c^2}r \delta(r-r_0) R ~=~ F e^{ikr}.$$ This is only the radial part.

• If you provide more information, people will be more willing to help you:-). What have you tried? Where have you looked it up? Where did you find it? – Ferdinando Randisi Oct 29 '12 at 14:51
• Ok. This is the radial part of schrodinger equation in Cylindrical co-ordinates. I am solving the potential scattering problem, the potential is potential barrier. I tried it with mathematica, but could get the solution. It was tried to solve in mathematics also without source term [RHS]. But now there is the source as the plane wave. – nagendra Oct 29 '12 at 15:09
• Yes, but what potential barrier? This is not a simple free particle confined in a sphere, is it? If it were, it should not have the $\delta$ term, if i remember correctly. Also, what is the $Fe^{ikr}$ term? If you tell us were the equation comes from, we might remember something about it. – Ferdinando Randisi Oct 29 '12 at 15:15
• Actually, the equation has the derivative of the potential and the potential is v(r) = vo in 0<r<ro and 0 in r> ro. At r = ro the derivative turns out to be d_function. The term in RHS is the source term, the plane wave. Actually, this equation is around r = ro. Derivative is spatial derivative. – nagendra Oct 29 '12 at 15:28
• Right Hand Side is Plane wave. Does any one have any idea to solve this please? – nagendra Nov 21 '12 at 18:14