Figure 1
Difference between the numerical eigenvalues of ℋ and the state energies of the non-relativistic theory. Differences are plotted according to principal quantum number n according to basis parameter pairs nmax = 300 and k = 0.3 (blue, dashed line), nmax = 400 and k = 0.3 (red, dotted line), and nmax = 300 and k = 0.1 (green, solid line). The insert shows the same data over a smaller range of n.
Figure 2
An example of a successful convergence test. These heat-maps show the variation in calculated values under small changes in nmax and k for calculations around two different magic wavelengths: 514.6 nm (red) and 399.5 nm (blue). (a and b) show the variation in the calculated value of the magic wavelength; (c and d) the variation in the polarisability of the 2S state at each magic wavelength; and (e and f) show the variation in the inelastic photon rates for the 2S–1S transition. In all cases, the colour bar denotes the fractional change from the value calculated at nmax = 300 and k = 0.3.