| N |
| Spherical well | Hydrogen atom | Harmonic oscillator |
| 3 | π | 2.789 | 3 | 2.25 |
| 4 | 3.8317 | 4.894 | 5 | 4 |
| 5 | 4.4934 | 7.5635 | 7.5 | 6.25 |
| 6 | 5.1356 | 10.7915 | 10.5 | 9 |
| 7 | 5.7635 | 14.5725 | 14 | 12.25 |
| 8 | 6.3802 | 18.9021 | 18 | 16 |
| 9 | 6.9879 | 23.7770 | 22.5 | 20.25 |
| 10 | 7.58834 | 29.1943 | 27.5 | 25 |
| 15 | 10.5128 | 64.3398 | 60 | 56.25 |
| 20 | 13.3543 | 112.7790 | 105 | 100 |
| 30 | 18.9 | 249.07 | 232.5 | 225 |
| 40 | 24.338 | 437.446 | 410 | 400 |
| 50 | 29.7105 | 677.571 | 637.5 | 625 |
| 100 | 56.0729 | 2648.056 | 2525 | 2500 |
| 150 | 82.037 | 5893.356 | 2662.5 | 2625 |
| 200 | 107.808 | 10407.52 | 10050 | 10000 |
| 300 | 159.033 | 23230.498 | 22575 | 22500 |
| 400 | 210.0113 | 41101.582 | 40100 | 40000 |