Hello
It seems the value of reduced planck constant used is 1 in qutip. To use the effective value of hbar=a, I divided the Hamiltonian by a, and used the schrodinger solver in qutip package on that.
I hope that is correct. I actually needed to calculate wigner distribution with this effective hbar value for a coherent state with a given ,<x> and <p>. So I used this effective value of hbar with m and omega both 1, to get the real part and imaginary value of alpha for the coherent state.
Then for wigner distribution calculation, I used g value derived from this effective hbar.
I hope this approach is correct.
Sudipta