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A direct application of the WKB quantization to the three-dimensional Coulomb potential does not yield the exact eigenenergies. The three-dimensional Coulomb potential is converted to a Morse potential by using the point canonical transformation. Then the WKB quantization is applied to the Morse potential to find a relationship between the eigenenergies of the Coulomb and those of the Morse potentials. From the relationship the exact eigenenergis of the Coulomb potential are determined. The same method is found to be also valid for the three-dimensional harmonic oscillator potential. And the Langer modified WKB quantization is algebraically derived.

Eigenenergies of 3D-Coulomb and 3D-Harmonic Oscillator Potentials from WKB Quantization: Point Canonical Transformation