The energy spectra of spherically confined hydrogen atom embedded in an exponential-cosine-screened Coulomb potential is worked out by using the Bernstein-polynomial method. The interaction of short laser pulses in the femtosecond range with the system is studied in detail. The effect of shape of laser pulse, confinement radius, Debye screening length as well as different laser parameters on the dynamics of the system has been explored and analyzed.

The generation of charge currents and hence induced magnetic field in a spherically bound hydrogen atom by an ultrafast right circularly polarized laser pulse has been studied. The atom is assumed to be under the effect of a Hulthén plus a ring-shaped potential. The simultaneous effect of pulse parameters such as E _{l 0} , t _p and ω ₀ , the cavity radius, r ₀ , and parameters related to the non-central potential has been investigated. These parameters have been found to significantly affect the magnitude of generated current as well as the magnetic field and thus play an important role in determining the response of the system to external laser. The laser pulse is found to produce femtosecond magnetic pulses. Such magnetic pulses have many biomedical applications. Hulthén screening or ring deformation potential reduces the magnitude of current and induced magnetic field for an unbounded atom. On the other hand, for the bounded case, the potential parameters are found to have a positive impact on these quantities.

Transitions of an atom under the effect of a Gaussian potential and loose spherical confinement are studied. An accurate Bernstein-polynomial (B-polynomial) method has been applied for the calculation of the energy levels and radial matrix elements. The transition probability amplitudes, transparency frequencies, and resonance enhancement frequencies for transitions to various excited states have been evaluated. The effect of the shape of confining potential on these spectral properties is studied.