Abstract
The authors show how explicit use of the constraint equation that arises when the Kustaanheimo-Stiefel transformation (1965) is applied to the hydrogen atom in R3 enables them to determine the wavefunctions for the constrained harmonic oscillator in R4 with the correct restriction on the quantum numbers in a direct and natural manner. They then highlight and resolve a discrepancy between the R4 oscillator wavefunctions produced by different authors by considering the measure to be used in R4 and the operator ordering in the quantised Hamiltonian.