# Effective Polar Potential in the Central Force Schr¨ odinger Equation 

Physics Program, Middle East Technical University North Cyprus Campus Guzelyurt, TRNC 

M.S.Shikakhwa ∗ † and M.Mustafa ‡ 

via Mersin 10, Turkey 

## Abstract 

The angular part of the Schr¨ odinger equation for a central potential is brought to the one - dimensional ”Schr¨ odinger form” where one has a kinetic energy plus potential energy terms. The resulting polar potential is seen to be a family of potentials characterized by the square of the magnetic quantum number m . It is demonstrated that this potential can be viewed as a confining potential that attempts to confine the particle to the xy -plane, with a strength that increases with increasing m . Linking the solutions of the equation to the conventional solutions of the angular equation, i.e. the associated Legendre functions , we show that the variation in the spatial distribution of the latter for different values of the orbital angular quantum number l can be viewed as being a result of ”squeezing” with different strengths by the introduced ”polar potential”. PACS numbers: 

