"With the growing importance of models in statistical mechanics and in field theory, the path integral method of Feynman was soon recognized to offer frequently a more general procedure of enforcing the instead of the Schrödinger equation. To what extent the two methods are actually equivalent, has not always been understood... [T]here are few nontrivial models which permit deeper insight into their connection. However, the exactly solvable cases... the Coulomb potential and the harmonic oscillator... point the way: For scattering problems the path integral seems particularly convenient, whereas for the calculation of discrete eigenvalues the Schrödinger equation [is preferable]. ...[P]otentials with degenerate vacua ...arise ...in recently studied models of large spins."