Inserting this wave function into the expression for the local energy E_L gives E_L(\rho)=-\frac{1}{\rho}- \frac{\alpha}{2}\left(\alpha-\frac{2}{\rho}\right). A simple variational Monte Carlo calculation results in
| \alpha | \langle H \rangle | \sigma^2 | \sigma/\sqrt{N} |
| 7.00000E-01 | -4.57759E-01 | 4.51201E-02 | 6.71715E-04 |
| 8.00000E-01 | -4.81461E-01 | 3.05736E-02 | 5.52934E-04 |
| 9.00000E-01 | -4.95899E-01 | 8.20497E-03 | 2.86443E-04 |
| 1.00000E-00 | -5.00000E-01 | 0.00000E+00 | 0.00000E+00 |
| 1.10000E+00 | -4.93738E-01 | 1.16989E-02 | 3.42036E-04 |
| 1.20000E+00 | -4.75563E-01 | 8.85899E-02 | 9.41222E-04 |
| 1.30000E+00 | -4.54341E-01 | 1.45171E-01 | 1.20487E-03 |