Effective polar potential in the central force Schrodinger equation. (arXiv:1001.3693v1 [quant-ph])

The angular part of the Schrodinger equation for a central potential is
brought to the one-dimensional 'Schrodinger 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'.

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Original source : http://arxiv.org/abs/1001.3693...