In this work, the spin-averaged mass spectra of heavy quarkonia and 𝐵𝐵 𝑐𝑐 mesons in a Cornell potential is studied within the framework of nonrelativistic Schrödinger equation. The energy eigenvalues and eigenfunctions are obtained in compact forms for any l-value using Nikiforov-Uvarov method. Based on the results determined the mass spectra of charmonium, bottomonium and 𝐵𝐵 𝑐𝑐 mesons. Our results are in good correspondence with other experimental and theoretical studies.

The Schrödinger equation for a potential being the sum of a harmonic oscillator potential, a linear potential, and a Coulomb potential has been solved by the Nikiforov-Uvarov method for large and small distances between particles being in the bound state. Asymptotic expansions have been obtained for the energy levels and wave functions, and also the wave function and the energy of the ground state have been found. The mass spectrum of heavy quarkonia and their radius have been calculated.

The generalized and static polarizabilities of charged pions, which are considered a relativistic sys tem of two pointlike spinor quarks with a linear interaction potential, are calculated. The relationship between static electricity and generalized polarizabilities of pions is studied in the context of this approach.

Keywords: perturbation theory, wave function of a coupled system, electric polarizability.The electromagnetic hadron characteristics can be determined with allowance for their quark structure based on the equation of motion of a compound system in an external electromagnetic field. The electric polarizability is one of such characteristics. To determine the electric polarizability, it is necessary to solve the Schrödinger equation for a coupled system in an external electric field.Though modern methods of solving equations for coupled systems are insufficiently exact for calculations, but they enable one to calculate the wave function of the ground state of the examined system. An approximate solution is reduced to calculations of corrections to the wave function.Calculations of corrections to the wave functions by the Rayleigh-Schrödinger method require knowledge of all eigenfunctions of the unperturbed equation. In the case of the potential interaction, however, the method described in [1], according to which the unperturbed equation is solved only for one energy value, can be used. As a result, the correction to the wave function of an arbitrary discrete state is expressed in terms of the unperturbed wave function of this state. Unlike the Rayleigh-Schrödinger perturbation theory, this obviates the need for the knowledge of the entire state spectrum for the unperturbed problem.In the present work, the correction to the wave function of relative coupled system motion in an external electric field is calculated in the context of Ya. B. Zel'dovich's perturbation theory, and the π -meson polarizability is calculated for the nonrelativistic quark model of the Coulomb potential of quark and antiquark interaction.

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