  The comparison of the Hamiltonians of the noncommutative isotropic harmonic
oscillator and Landau problem are analysed to study the specific conditions
under which these two models are indistinguishable. The energy eigenvalues and
eigenstates of Landau problem in symmetric and two Landau gauges are evaluated
analytically. The Hamiltonian of a noncommutative isotropic harmonic oscillator
is found by using Bopp's shift in commutative coordinate space. The result
shows that the two systems are isomorphic up to the similar values of $n_{r}$
and $m_{l}$ and $qB = eB > 0$ for both gauge choices. However, there is an
additional requirement for Landau gauge where the noncommutative oscillator has
to lose one spatial degree of freedom. It also needs to be parametrized by a
factor $\zeta$ for their Hamiltonians to be consistent with each other. The
wavefunctions and probability density functions are then plotted and the
behaviour that emerges is explained. Finally, the effects of noncommutativity
or magnetic field on the eigenstates and their probability distribution of the
isomorphic system are shown.
