Subcritical External Potentials

Abstract

To prepare for the discussion of overcritical phenomena in the case of spin-0 particles, in this chapter the quantized theory of bosons in external potentials will be treated. Starting from the Hamiltonian field equations and the commutation relations for the field operators, the standard procedure of canonical quantization is outlined. This leads to the construction of the many-particle Fock space and to diagonalized expressions for the charge operator and the Hamiltonian. Finally the energy spectrum of the Klein-Gordon equation with a point-like Coulomb potential is obtained. It is found to exhibit singular behaviour already at Zα= 1/2.