  We describe a multi-scale resolution approach to analyzing problems in
Quantum Mechanics using Daubechies wavelet basis. The expansion of the
wavefunction of the quantum system in this basis allows a natural
interpretation of each basis function as a quantum fluctuation of a specific
resolution at a particular location. The Hamiltonian matrix constructed in this
basis describes couplings between different length scales and thus allows for
intuitive volume and resolution truncation. In quantum mechanical problems with
a natural length scale, one can get approximate solution of the problem through
simple matrix diagonalization. We illustrate this approach using the example of
the standard quantum mechanical simple harmonic oscillator.
