Table 7: Approximate energy levels for a confined sine squared potential in dimension . For the state , denotes the upper bound for the energies obtained using the present variational analysis with basis size and fixed . The table shows the energies of the first states .

0 1.024922118883 1.242428825987 2.082985293205 1 4.049947916808 4.494793078632 6.370661125009 2 9.050038818610 9.503664867046 11.569339156939 3 16.050020833189 16.502081901038 18.551201398403 4 25.050013020839 25.501302132228 27.532566336109 5 36.050008928573 36.500892873766 38.522331587359