Table 5: Approximation of the energy levels of the hydrogen atom in dimension , for quantum numbers . Note that the variational parameter that minimizes the upper bound tends to be very large for all the states. The error is of the order of in the “best” cases.


0
1 −0.2500000000 −0.2499790730 17.5
2 −0.06250000000 −0.06246859682 40.5
3 −0.02777777778 −0.02773301831 70.5
4 −0.01562500000 −0.01556528040 107
1
1 −0.06250000000 −0.06231120892 33
2 −0.02777777778 −0.02747649731 60
3 −0.01562500000 −0.01526320869 94
4 −0.01000000000 −0.009656788911 143
2
1 −0.02777777778 −0.02777640178 75
2 −0.01562500000 −0.01561644406 108
3 −0.01000000000 −0.009970374676 146
4 −0.006944444444 −0.006872824074 189