With a given number of steps, $n_{\mathrm{step}}$, we then define the step $h$ as $$h=\frac{\rho_{\mathrm{max}}-\rho_{\mathrm{min}} }{n_{\mathrm{step}}}.$$ Define an arbitrary value of $\rho$ as $$\rho_i= \rho_{\mathrm{min}} + ih \hspace{1cm} i=0,1,2,\dots , n_{\mathrm{step}}$$ we can rewrite the Schr\"odinger equation for $\rho_i$ as $$-\frac{u(\rho_i+h) -2u(\rho_i) +u(\rho_i-h)}{h^2}+\rho_i^2u(\rho_i) = \lambda u(\rho_i),$$ or in a more compact way $$-\frac{u_{i+1} -2u_i +u_{i-1}}{h^2}+\rho_i^2u_i=-\frac{u_{i+1} -2u_i +u_{i-1} }{h^2}+V_iu_i = \lambda u_i,$$ where $V_i=\rho_i^2$ is the harmonic oscillator potential.