In this work we study two types of quantum systems confined in the space limited by a barrier of infinite potential: the unidimensional harmonic oscillator and the hydrogen atom. The two systems are of the great importance in the study of physical properties of quantum systems, such as the vibrational spectrum of molecules in solids and the spectrum of energy for an atom model under pressure. For both systems are obtained analytical solutions to the free and confined situations through the imposition of boundary conditions on the wave function. The energy spectrum of the confined system is obtained by the implementation of computational programs that they research the roots of a polynomial. The obtained results show different effects that happen in confined systems, allowing to do a comparison with free systems.
spatial confinement; harmonic oscillator; hydrogen atom
