  We apply the Born-Jordan and Weyl quantization formulas for polynomials in
canonical coordinates to the constants of motion of some examples of the
superintegrable 2D anisotropic harmonic oscillator. Our aim is to study the
behaviour of the algebra of the constants of motion after the different
quantization procedures. In the examples considered, we have that the Weyl
formula always preserves the original superintegrable structure of the system,
while the Born-Jordan formula, when producing different operators than the
Weyl's one, does not.
