We investigate the linear response of a nonrelativistic hydrogenlike atom to a harmonic uniform electric field, which is switched on adiabatically. For the electron initially in an arbitrary bound \ensuremath{\Vert}nlm〉 state, the first-order correction to the wave function has been written in terms of a vector function
wnlm. We report an exact closed-form expression of the vector
wnlm that we have derived using the Coulomb Green's function. Our general analytic results prove to be useful in a systematic study of two-photon processes involving the hydrogen atom.
We discuss the arising of bound states solutions to the Schrödinger equation due to the presence of a Coulomb-type potential induced by the interaction between a moving particle possessing an electric quadrupole moment and an electric field. Besides, we study the influence of the Coulomb-type potential on the harmonic oscillator by showing a quantum effect characterized by the dependence of the angular frequency on the quantum numbers of the system. Finally, we consider the quantum particle subject to harmonic and linear confining potentials and investigate the influence of the analogue of the Coulomb potential.
The quantum dynamics of an atom with a magnetic quadrupole moment that interacts with an external field subject to harmonic and linear confining potentials is investigated. It is shown that the interaction between the magnetic quadrupole moment and an electric field gives rise to an analogue of the Coulomb potential and, by confining this atom to harmonic and linear confining potentials, a quantum effect characterized by the dependence of the angular frequency on the quantum numbers of the system is obtained. In particular, it is shown that the possible values of the angular frequency associated with the ground state of the system are determined by a third-degree algebraic equation.