% \font\secf=cmbx12 scaled\magstep2
%\font\subf=cmbx12

For the Nelson potential, we have
%%      /* V = mu*x^2/2 + (y - x^2/2)^2 */

$$ V = \mu {x^2 \over 2} + \left( y - {x^2 \over 2} \right) ^2 $$

``Good'' values of parameters seem to be [Baranger]

$$\eqalign{
\mu   &= 0.1\cr
m     &= 1\cr
\hbar &= 0.05\cr
E_{\hbox{clas}} &= 0.5\cr
}$$

\centerline{\vbox{\hrule width 2in}}

for HOP:

$$ \hat H = \hat T + \hat V = {1\over2m} \left( p_x^2 + p_y^2 \right) 
                           + k {x^2\over2} + k {y^2\over2} $$

for Nelson:

$$ \hat H = \hat T + \hat V = {1\over2m} \left( p_x^2 + p_y^2 \right) 
              + \left( \mu {x^2\over2} + \left( y - x^2/2 \right)^2 \right) $$
