on the evolution of $M_L$. A canonical estimate in the galactic context (see Zeldovich et al. 1983) is $\alpha_N \sim 2C(0)  \sim (V^2\tau /h)(\Omega\tau) \sim \Omega \tau V(L/h)$ and $\kappa_N \sim T_{LL}(0) \sim V^2\tau \sim VL$. Here where $h$ is the disk scale height, $\Omega$ the rotation frequency, $V$, $\tau$ and $L$ are the velocity, correlation time, and correlation lengths for the energy carrying eddies of the turbulence. Assuming $H\sim M_L/h$, the importance of the coupling term $\alpha_N H$ in Eq. (\[mleq\]) to the other terms is $\sim (\alpha_NH/(\kappa_N M_L/L^2)) \sim
\Omega\tau (L/h)^2 << 1$ in general. (Even for $\tau \sim L/V$ we generally have $\Omega\tau <<1$). So it is an excellent approximation to neglect the coupling to $H$ in examining evolution of $M_L$. We will refine this estimate in the next section after studying the evolution of $H$ and see that the above approximation is even better.

The evolution for $M_L$ can then be transformed into a Schrodinger-type equation by defining $\Psi =r^2\sqrt{\kappa_N}M_L$. We get $${1\over 2}{\partial \Psi \over \partial t} = 
\kappa_N{\partial^2 \Psi \over \partial r^2} - U(r,t)\Psi \label{sievol}$$ where for a divergence free velocity field, the “potential” $$U(r,t) =  T_{LL}^{\prime\prime} + {2 \over r} T_{LL}^{\prime} 
+ {\kappa_N^{\prime\prime} 