2012, Vol.15, No.2, pp.163-170
It is shown that the Schrödinger equation with a potential in the form of a combination of
three potentials Coulomb, linear and harmonic, the potential often used to describe
quarkonium, is reduced to a bi-confluent Heun differential equation. The method to construct its solutions in the form of polynomials is developed,
however with additional constraints in four parameters of the model, .The energy spectrum looks as a modified combination
of oscillator and Coulomb parts.
Key words:
Schrödinger equation, quarkonium, Heun differential equation
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