Table 8: Approximation of the energy levels of a confined hydrogenic atom in dimension . The angular-momentum quantum number is , is plus the number of nodes of the radial wave function, is the radius of the box, is the exact value of the energy, is the expression in floating point arithmetic, and is the variational approximation obtained from the matrix H of dimension .


0 1 4 −1/16 −0.06250000000 −0.0624999668
1 1 12 −1/36 −0.02777777778 −0.0277777498
2 1 24 −1/64 −0.01562500000 −0.0156250000
3 1 40 −1/100 −0.01000000000 −0.0100000000
0
1 −1/36 −0.02777777778 −0.0277777466
2 −1/36 −0.02777777778 −0.0277775785
1
1 −1/64 −0.01562500000 −0.0156249729
2 −1/64 −0.01562500000 −0.0156248833
2
1 −1/100 −0.01000000000 −0.0100000000
2 −1/100 −0.01000000000 −0.00999999997
3
1 36 −1/144 −0.006944444444 −0.006944444438
2 72 −1/144 −0.006944444444 −0.006944444431