Lagrange multipliers in the cranked harmonic oscillator model

The Lagrange multipliers associated with the cranked harmonic oscillator model are studied. The coefficient of L₁ in the minimization procedure is shown to be generally not simply equal to ω as it is usually taken. When the proper Lagrange parameters are used in the pure oscillator model the proportionality between the axis of the potential and the axis of the density results. If an incorrect multiplier is used a calculation shows that a pathologic behaviour of the nucleus may result.