The Schrödinger equation in a 2D cylindrical coordinate system is numerically solved for the ground state and a few excited states of the hydrogen atom in arbitrary magnetic fields. The second order discretization of the PDEs on finite volumes results in a set of algebraic equations that are solved simultaneously using Gauss-Seidel Algebraic Multi-Grid (AMG) solver. The modified Stodola-Vianello method is implemented using Gram-Schmidt orthogonalization process to extract the first few energy states and their wave functions concurrently. A detailed mesh convergence study suggests that both energies and wave functions correctly approach toward the unknown exact solutions.

The general formalism of the Modified orbital atomic theory (MAOT) for the Rydberg series of atoms and ions is presented. Energy resonances of the $2s^22p^4(^1D_2)ns,$ $nd,$ $2s^22p^4(^1S_0)ns,$ $nd$ and $2s^2p^5(^3P_2)np$ Rydberg series originating from the $2s^22p^{5}$ $^2P_{1/2}$ metastable and from the $2s^22p^{5}$ $^2P_{3/2}$ ground state of $Ne^+$ are tabulate applying the MAOT formalism. Analysis of the present results is achieved in the framework of the standard quantum defect expansion formula. Comparison is done with the existing experimental and theoretical data.

The effect of impurity atoms on structures, stabilities and electronic properties of $MSn_{10} (M= Li, Be, B and Ca)$ clusters have been investigated using the density functional theory based B3LYP method with cc-pVTZ(-PP) basis set. The results show that the location of the impurity atom depends on the interactions of impurity atoms with the host cluster and the size of the impurity atom itself. The stability has been analyzed based on average binding energy, vertical ionization potential, vertical electron affinity, HOMO - LUMO energy gap and embedding energy. Several clusters, such as $BeSn_{10},$ $Sn_{10}$ and $Sn^{(2-)}_{10}$ with enhanced stability have been identified. The stability of $Sn_{10}(C_{3v})$ can be rationalized using the jellium shell model. Molecular orbital analyses reveal that the enhanced stability of $BeSn_{10}$ and $Sn^{(2-)}_{10} (D_{4d})$ with 42 valence electrons may arise from a crystal-field splitting of the 1G shell and from the closed-shell nature of the $\pi$ subsystem, which is subjected to the $2(N_{\pi}+1)^2$ rule with $N_{\pi}=1.$ Both $BeSn_{10}$ and $Sn^{(2-)}_{10}$ clusters can be considered to be aromaticity with $8\pi$ electrons, further confirmed by the large nucleus-independent chemical shift values.

Clusters are well known for their extensive applications in various fields as their properties are quite different from their bulk analog. In the present study, we have investigated various conformers of $Nb_nS_m (n,m=1, 2)$ clusters in their neutral as well as anionic and cationic states. Their stabilities are discussed by calculating binding energies per atom and fragmentation energies against dissociation to $S$ atom. The electronic properties are also explored for all the species.

The quenching of the photoinduced excited triplet of 9,10-anthraquinone $(^3AQ^*)$ by Vitamin C (VC) has been studied in ethylene glycol-water $(EG-H_2O, EG/H_2O=9/1, v/v)$ homogeneous by using time-resolved electronic paramagnetic resonance (TR-EPR) and laser flash photolysis techniques. According to the chemically induced dynamic electron polarization (CIDEP) and transient absorptive spectra, the reaction intermediates and the reaction mechanism have been analyzed. The rate constant for the quenching of excited triplet $^3AQ^*$ by VC has been measured. The results indicate that $^3AQ^*$ can capture hydrogen atom not only from ethylene glycol molecule but also from VC. The strong CIDEP signal of VC monoanion radical indicates that the quenching of VC to $^3AQ^*$ is obvious. The rate for the quenching of $^3AQ^*$ by VC is nearly diffusion-controlled.

A novel cyclometalated iridium complex bis[(4-(2-(4-Diphenylamino-phen yl)-benzoinidazol-1-ylmethyl)-phenyl)-diphenyl-amine]iridium(acetylacetonate) Ir(DBPA)$_2$(acac) is designed and synthesized, and the thermo-stability and photo-physical properties of iridium complex Ir(DBPA)$_2$(acac) are researched in detail. The complex is functionalized by a bulky non-planarity substituent, thus the phosphorescent concentration quenching in solid state is substantially suppressed, and Ir(DBPA)$_2$(acac) exhibits bright green-emitting in both solution and solid. The maximum emission peak inr pure solid is about 516 nm, which is slightly blue-shifted in comparison with that in solution. Moreover, the complex Ir(DBPA)$_2$(acac) exhibits high photoluminescent efficiency and short excited lifetime, indicating it has potential application in fabricating nodoped electrophosphorescence device.

By numerically solving the Maxwell-Bloch equations using an iterative predictor-corrector finite-difference time-domain (FDTD) technique, the optical limiting (OL) and two-photon absorption (TPA) properties for femtosecond laser pulses in a strong TPA organic molecular (4,4'-bis (di-n-butylamino) stilbene (BDBAS))medium are studied. The medium has obvious OL behavior in a certain intensity region which is dependent on the propagation distance, sample concentration, input pulse width and effect of optical ionization. Moreover, dynamical TPA cross sections are obtained, showing an increasing trend with the broadening of the pulse width and the propagation distance in the femtosecond time domain.

By employing the linear combination operator and the unitary transformation methods, we study the vibrational frequency and the ground state energy of a strong-coupling polaron in symmetric RbCl quantum dots (SRQDs). The effects of the temperature and the confinement strength are taken into account. It is found that the vibrational frequency and the ground state energy are increasing functions of the temperature and the confinement strength. We find two ways of tuning the vibrational frequency and the ground state energy via adjusting the temperature and the confinement strength.

The main aim of this paper is to discuss the electrodynamics of relativistic dynamics of particles bases on the notion of the non-standard Lagrangians which have gained increasing importance in the theory of nonlinear differential equations, dissipative dynamical systems and theoretical physics. The mathematical settings are constructed starting from the modified Euler-Lagrange equation and modified Hamiltons equations. Some illustrative examples are considered and discussed.