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o cases, as well as other intermediate situations, are discussed within this section.

In particular, the ground state energy of this kind of system is calculated for different confining situations. Moreover, the behavior of the ground state energy is analyzed, as the confining region reaches an extreme value, that is, when the system becomes quasi-one-dimensional (open curves) or quasi-zero-dimensional (closed curves) as well as other intermediate situations.

The results show a very interesting behavior of this property depending upon the confinement region as well as the closed or open character of the curves.

The latter would represent an interesting research topic concerning the study of other properties of this system such as its polarizability, pressure due to the boundaries, dipole moment, etc.

4.1.1. Schrödinger Equation

In atomic units (h = e = m*e = 1), the Schrödinger equation for the two-dimensional confined hydrogen atom in orthogonal curvilinear coordinates can be written as

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