FIG. 1: Graphs of the potential for several values of integer m are special cases of the so called P¨ oschl-Teller potential [3, 4] . To gain a closer look at the potential, we plot it for various m -values in Fig.1. As the figure intuitively suggests, the potential, which is infinite at the boundaries - thus banning the particle from going beyond the boundary- attempts to confine the particle about the z -axis, the higher m is the stronger is the confining strength. For the lower m values the potentials are very close to an infinite well with width π , as we increase m the potential squeezes the states resulting in more confinement. Let’s take a look at the solutions now. The solutions for this family of potentials can be worked out in several ways, a nice algebraic way is to use Infeld and Hull factorization method [5]. This family of potentials enjoys shape invariance symmetry, which can be exploited to workout the eigenvalues algebraically. Supersymmetric quantum mechanics techniques can also be used to work out the eigenstates [6]. We will not use these techniques here, rather we will work out the solutions from the solutions of the original angular equation (6). If we restrict the values of m to nonnegative integers, the solutions, upon employing the transformation (11) can be written directly from the solutions of the original equation and they read where P m n + m are, again, the associate Legendre functions. These solutions are for non- negative m , those for negative m are - as is well-known [1, 2]- directly proportional to these y m n ( θ ) = N m n sin 1 2 θ P m n + $_{m}$(cos θ ) (13) 5