Table 1: Properties of one-body semiclassical spectrum labeled by the integer j for four solvable potentials in D dimensions. The well-depth and the range R of the rectangular, linear, and oscillator wells are made finite using the unit step function. The Coulomb well is left unrestricted over all r. For other notations, see Appendix A. (We do not tabulate the rigid box potential model which has the upper end of the energy spectrum at Such a model is of little interest in cosmology In usual physical applications, one puts )

PotentialRectangularLinearOscillatorCoulomb

Form
Highest label
Ionization threshold 000
Spectrum
Turning point
Separation
Geometrical coefficient
Accumulated states
Level degeneracy