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It is shown that Schr\"odinger equation with combination of three potentialsU = - {\alpha} r^{-1} + {\beta} r + kr^{2}, Coulomb, linear and harmonic, thepotential often used to describe quarkonium, is reduced to a bi-confluent Heundifferential equation. The method to construct its solutions in the form ofpolynomials is developed, however with additional constraints in fourparameters of the model, {\alpha}, {\beta}, k, l. The energy spectrum looks asa modified combination of oscillator and Coulomb parts.

On Schr\"odinger equation with potential U = - {\alpha}r^{-1} + {\beta}r + kr^{2} and the bi-confluent Heun functions theory