The variational method is used to calculate the ground state energy of the hydrogen atom confined within hard spherical and cylindrical surfaces, for an atomic nucleus which is off the center of symmetry of the confining boundary. It is shown that the wave function for the free hydrogen atom in spherical coordinates (referred to the center of symmetry of the confining geometry) can be used without further assumptions to construct the trial wave function systematically. The latter is assumed to be the product of the free wave function and a simple cutoff function that satisfies the appropriate boundary conditions. We compute the ground state energy for these systems and the results are in good agreement with more sophisticated calculations, thus proving the reliability of the proposed strategy.
Electron states in a magnetic quantum ring are investigated. The
electron is assumed to be confined to a plane in the presence of a
magnetic field which is zero within the ring a
Optical properties of asymmetrical multiple quantum wells for the construction of quantum cascade lasers are calculated, and expressions for the electronic states of asymmetrical multiple quantum wells are presented. The gain and differential cross-section for an electron Raman scattering process are obtained. Also, the emission spectra for several scattering configurations are discussed, and the corresponding selection rules for the processes involved are studied; an interpretation of the singularities found in the spectra is given. The electron Raman scattering studied here can be used to provide direct information about the efficiency of the lasers.
The ground state and binding energies for a hydrogenic impurity in a spherical quantum dot within a uniform magnetic field, are calculated through the variational method in the frame of the effective-mass approximation. The trial wave functions used in the calculation are flexible enough to treat the cases of on-center, off-center, or edge impurities. Overall results show reasonable agreement when compared with other calculations. Interestingly enough, in the case of an off-center impurity, a critical point from which bulk states evolve to surface or edge states is also found. The dependence of this point on the magnetic field strength is discussed and interpreted.
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