Discrete spectrum for a system of electrically charged particles

For a system of electrically charged particles, the time-independent Schrödinger’s equation is transformed into hyperspherical coordinates. By using the hyperharmonic expansion, the hyperradial equation is obtained, and its discrete spectrum is investigated. To this end, only negative energy values are taken into consideration. The functional equation which yields the discrete spectrum of the hyperradial equation is obtained by means of a matching technique in the Laplace transform domain of hyperradial Schrödinger’s equation.