  We analyze the classical equations of motion for a particle moving in the
presence of a static magnetic field applied in the $ z $ direction, which
varies as $ {1\over{x^2}} $. We find the symmetries through Lie's method of
group analysis. In the corresponding quantum mechanical case, the method of
spectrum generating $su(1,1)$ algebra is used to find the energy levels for the
Schroedinger equation without explicitly solving the equation. The Lie point
symmetries are enumerated. We also find that for specific eigenvalues the
vector field contains $ {1\over{x}} {{\p}\over{\p x}}$ and $ {1\over {x^2}}
{{\p}\over{\p {x}}}$ type of terms and a finite Lie product of the generators
do not close.
