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.