Table 6: Approximation of the energy levels of the harmonic oscillator in dimension . For the state , is a highly accurate solution for the energy provided by Aguilera-Navarro et al. [2], is the upper bound for obtained using the present variational analysis with basis size , and . This table shows the energies of the first states .


0 4.951123323264 4.951129323244
1 19.774534178560 19.774534179209
2 44.452073828864 44.452073829725
3 78.996921150976 78.996921150748
4 123.410710456832 123.410710456280
5 177.693843822080 177.693843818558
6 241.846458758144 241.846458765623
7 315.868612673536 315.868612686280
8 399.760332976128 399.760332979135
9 493.521634054144 493.521634068796
10 597.152524107776 597.152524136545
11 710.653008064512 710.653008103290