Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), harmonic oscillator potential, Explicit solutions, first integrals of ordinary differential equations, Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.), Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc., Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics, Schrödinger equation, Special integral transforms (Legendre, Hilbert, etc.), Darboux transformation