Consider a one-dimensional asymmetrical potential well given by the potential with . The corresponding solution for the wave function with is found to be and The energy levels are determined once is solved as a root of the following transcendental equation where Existence of root to above equation is not always guaranteed, for example, one can always find a value of so small, that for given values of and , there exists no discrete energy level. The results of symmetrical well is obtained from above equation by setting . Spherical cavity The results above can be used to show that, as to the one-dimensional case, there is two bound states in a spherical cavity, as spherical coordinates make equivalent the radius at any direction. The ground state (n = 1) of a spherically symmetric potential will always have zero orbital angular momentum (ℓ = n−1), and the reduced wave function satisfies the equation where is the radial part of the wave function. Notice that for (n = 1) angular part is constant (ℓ = 0). This is identical to the one-dimensional equation, except for the boundary conditions. As before, The energy levels for are determined once is solved as a root of the following transcendental equation where Existence of root to above equation is always guaranteed. The results are allways with spherical symmetry. It fullfils the condition where the wave does not find any potential inside the sphere: See also Potential well Delta function potential Infinite potential well Semicircle potential well Quantum tunnelling Rectangular potential barrier References Further reading . Quantum mechanical potentials Quantum models