Table 2: The energy levels for the quartic anharmonic oscillator in dimension . represents the energy state, represents the accurate energy values obtained in [1], and is the upper bound to obtained using the present variational analysis in a basis of size . The eigenvalues of H were minimized over the box size, and is the optimal value obtained. The table shows the first states, .


0 1.3923516415 1.3923516415 3.4
1 4.6488127042 4.6488127042 3.4
2 8.6550499577 8.6550499586 3.4
3 13.1568038980 13.1568038994 3.7
4 18.0575574363 18.0575574558 3.4
5 23.2974414512 23.2974415625 3.4