  In this paper, we show that the Laughlin wave function is a Hamiltonian and
its associated Berry connection as the Schr\"odinger equation by transforming
the Schr\"odinger equation into the Kirchhoff equation which describes the
evolution of $n$ point vortices in Hydrodynamics. This helps us to view the
Berry connection associated with Laughlin wave function or Schr\"odinger
equation is not Hermitian, therefore we propose a self adjoint model
Hamiltonian for the fractional quantum Hall effect, from the study of Kirchhoff
equation, using superymmetric quantum mechanics whose solutions are complex
Hermite polynomials. The Schr\"odinger equation as Berry connection allows us
to formulate the problem of quantisation in terms of topology, as the quantum
numbers are topological invariant which arise due to singularities in the
Kirchhoff equation. Quantisation arises as it continuously connects the
topologically inequivalent Hamiltonians in the Hilbert space.
