solutions. So, without loss of generality, we will restrict ourselves to nonnegative m values. In the original equation (6), the solutions are conventionally labeled by a pair of numbers ( m , l ) and subject to the condition m ≤ l . The pairs ( m , l ) constitute a lattice as shown in Fig.2. In the conventional interpretation of the solutions of (6) the number l is associated with the angular momentum, so the usual way to look at the grid of solutions is to fix the angular momentum by fixing l and then changing m , so all the solutions with different m ’s and same l are degenerate and correspond to the same angular momentum. This amounts to moving right (or left) on the grid. But what we are doing here is different, we are fixing m and looking at the solutions of a one-dimensional potential at a fixed m value. When we fix the value of m to a specific integer we get all the solutions for that one dimensional potential. As one can see, the first eigenstate for m = 1 is at l = 1, but it still corresponds to the ground state of m = 1 potential, which will be labeled as n = 0, where n is the quantum number which labels the states of a fixed m potential. The same thing happens with all other m -values, thus we are moving up the grid shown in Fig.2. It is always the case that the ground state of a fixed m potential coincides with a l = m , therefore, the relation between l and n is l = m + n . Consequently, the eigenergies can now be written down directly from those of equation (12); they read: Here, higher values of n , i.e. excited states correspond to higher values of the kinetic energy of the confined particle. That this corresponds to higher l -values -in the conventional view- is natural, as higher kinetic energies mean higher angular momenta. E m n = 1 2 ( n + m + 1 2 ) 2 (14) FIG. 2: l and m lattice 6