In this paper we discuss the Sturm-Liouville theory, which has proven to be a useful tool when dealing with a variety of problems. Differential equations that often present themselves when modelling physical phenomena can be reduced to the problem of finding eigenvalues and eigenfunctions of a differential operator. It happens to be that the system comprised of all eigenfunctions is complete under certain conditions and that, therefore, each possible solution of the differential equation can be expressed as a linear combination of the eigenfunctions. We demonstrate this method of solving differential equations in the case of the Bessel equation, which we derive from the multidimensional wave equation. We also acquaint ourselves with the very basics of quantum mechanics and via the method of separation of variables solve the Schrödinger equation for the problem of quantum harmonic oscillator.
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