Bound States in Supercritical Fields and the Generalized Quantum Dynamics

The problem of the bound states in supercritical fields is investigated. A solution of the generalized dynamical equation is obtained, which determines the energy distribution of the electronic bound state $1s_{1/2}$, which is imbedded in the lower continuum, up to accuracy of $O((Z-Z_\mathrm{cr})/Z_\mathrm{cr})$, where $Z$ stays for the whole nuclear charge and $Z_\mathrm{cr}$ is the critical charge.