Via a special dimensional reduction, that is, Fourier transforming over one
of the coordinates of Casimir operator of su(2) Lie algebra and 4-oscillator
Hamiltonian, we have obtained 2 and 3 dimensional Hamiltonian with shape
invariance symmetry. Using this symmetry we have obtained their eigenspectrum.
In the mean time we show equivalence of shape invariance symmetry and Lie
algebraic symmetry of these Hamiltonians.Comment: 24 Page