  Integer and fractional quantum Hall effects were studied with different
physics models and explained by different physical mechanisms. In this paper,
the common physical mechanism for integer and fractional quantum Hall effects
is studied, where a new unified formulation of integer and fractional quantum
Hall effect is presented. Firstly, we introduce a 2-dimensional ideal electron
gas model in the presence of strong magnetic field with symmetry gauge, and the
transverse electric filed $\varepsilon_2$ is also introduced to balance Lorentz
force. Secondly, the Pauli equation is solved where the wave function and
energy levels is given explicitly. Thirdly, after the calculation of the
degeneracy density for 2-dimensional ideal electron gas system, the Hall
resistance of the system is obtained, where the quantum Hall number $\nu$ is
introduced. It is found that the new defined $\nu$, called filling factor in
the literature, is related to radial quantum number n and angular quantum
number $|m|$, the different $n$ and $|m|$ correspond to different $\nu$. This
provides unification explaination for integer and fractional quantum Hall
effects. It is predicated that more new cases exist of fractional quantum Hall
effects without the concept of fractional charge.
