Exact solution of the non-Hermitian eigenvalue problem for electron orbital excitations in a hydrogen atom

A new way of solving the spectral problem for description of electronic excitations is demonstrated for a hydrogen atom. The applied methodology is based on the idea of the electronic excitations description without introducing boundary conditions to the eigenvalue problem for the square of the angular momentum operator. The eigenvalues of such an operator are considered as complex in general. As a result, the spectral problem for the Schrödinger equation becomes non-Hermitian with complex energy values. The imaginary part of the total energy helps to estimate the excitation lifetime within a unified scheme. The existence of the Stark shift of atomic energy levels and the collapse of the atomic spectra are confirmed.