Semiclassical calculation of quantum energy levels using variational principles: application to He@C70

The reformulated Maupertuis variational principle is used in a semiclassical calculation to obtain the quantum energy levels of a nonseparable oscillator potential approximating the endohedral fullerene complex He @C70 The results are compared with levels obtained from a purely quantum mechanical, numerical calculation and are found to agree to better than 1% over at least the lowest 600 levels. The semiclassical calculation is found not to produce some level splittings seen in the purely quantum mechanical results. A simple modification of the calculation is described whereby the splittings may be predicted.