In this article, a four-particle quantum system is introduced with
energy discrete spectrum including a harmonic potential and a three-body
interaction potential. By defining the Jacobi coordinates for each
particle, separately, one coordinate is eliminated as a transition in
the energy spectrum. Then the system is studied in polar coordinates and
by using the variables separation method, the schrödinger equation of
the system is transformed into three separate differential equations.
Therefore, energy eigenvalues and wave eigenfunctions are calculated in
each dimension. Also, The wave eigenfunctions figures are investigated
in one and three dimensions.