In conclusion, we shown that the Laughlin wave function is the exact solution to the Schr¨odinger like equation for the harmonic oscillator potential. We have also shown that Harmonic oscillator can be written as the Laughlin wave function for simple poles. In the process we identify the quantum mo mentum function of quantum Hamilton Jacobi for malism with the Berry’s connection. This allowed us to formulate the problem of quantization in terms of topology, as the quantum numbers are topologi cal invariants arise due to singularities in the quan tum momentum function. The quantization is arising due to continuously connecting the topologically inequivalent Hamiltonians in the Hilbert space.
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