We propose a numerical scheme for two-dimensional hyperbolic telegraph equation, in which Chebyshev-Gauss-Lobatto collocation nodes and approximate solutions with multi-variable barycentric Lagrange interpolation functions are used. Multi-variable barycentric Lagrange interpolation functions are given for spatial, temporal variable and their derivatives. Accuracy of the method is demonstrated with test examples with Dirichlet and Neumann boundary conditions. Numerical results are more accurate than numerical solutions in literatures. In additional, the method is easy to implement for multidimensional problems.

We investigate effect of atomic densities (N) on propagation and spectral property of femtosecond Gaussian pulses in a three-level Λ-type atomic medium by using numerical solution of full Maxwell-Bloch equations.It is shown that,for pulses with smaller area 2π,propagate in mediums with different N,pulse splitting does not occur and strength of spectral component near central frequency decreases considerably as N increases.For pulses with area 4π,pulse splitting could occur when pulses propagate in dilute medium with greater atomic density and in dense medium,and pulse spectral bandwidth and strength of spectral component with higher frequency increase with increasing of N in dilute medium.Spectrum broadening in dense medium is much smaller than that in dilute medium with greater atomic density.For pulses with larger area 8π,pulse splitting is similar to that of 4π pulses.Pulse spectral bandwidth and strength of spectral component with higher frequency increase monotonously with increasing of N.And spectrum broadening in dense medium is much larger than that in dilute medium with smaller atomic density.

Electronic structure of BaMgF₄ crystal containing F color centers is studied within the framework of fully relativistic self-consistent Dirac-Slater theory,using a numerically discrete variational(DV-X_α) method.2p state of H atom is added into the program.It is concluded that energy levels of F color center are located in forbidden band of the crystal.Optical transition energy from ground state to excited state of the F color center is 5.12 eV,which corresponds to 242 nm absorption bands.They are well consisted with experiments.Absorption bands resulted from an F color center in BaMgF₄ crystal are located in 236-274 nm.

Electronic structures of possible F-type color centers in PbMoO₄ crystals are studied within the framework of a fully relativistic selfconsistent Dirac-Slater theory with a numerically discrete variational (DV-Xα) method. The results show that:F and F⁺ centers result in donor energy levels in forbidden band; optical transition energies are 2.141 eV and 2.186 eV, corresponding to 518 nm and 567 nm absorption, respectivly. The 580 nm absorption band after photo-chromic effect results from F-type color centers in PbMoO₄.