Spectrum and collapse of a particle in the field proportional to the squared secant of distance

The investigated problem is the one-dimensional Schroedinger equation with the singular potential proportional to the squared secant of the argument and the zero boundary conditions at the ends of the segment [0, π/2]. For this problem, the dependence of the spectrum of real eigenvalues large in absolute value and the corresponding eigenfunctions on the potential real parameter is analyzed. Special attention is paid to the particle collapse.