The canonical function method (CFM) is a powerful accurate and fast method that solves the Schrodinger equation for the eigenvalues directly without evaluating the eigenfunctions. In this work, it is applied to the solution 1D Schrodinger equation specializing to the linear potential that is perturbed by electric field. The linear and square Stark effects are perturbation terms. Finally, the CFM results will be compared with the exact results. The CFM method is superior to many standard techniques that have been used to solve the Schrodinger equation such as Numervo.

In this paper, due to the importance and abundant applications of carbon nanotubes doped with boron (CNT/B 2 O 3 ) in various industries with changes in the electrical, mechanical and chemical properties, mode identification and intensity of the Raman spectra of pure and boron oxide molecule-doped spectra have been performed. The main task in this paper is to monitor the alteration of the relevant vibrational mode intensities of the pure and B-doped samples. In experimental approach, by utilizing a simple method we synthesized CNT doped with B 2 O 3 using laser ablation in liquid environment technique. The silver nanoparticles were made by the Lee-Meisel method, and then the spontaneous and surface-enhanced Raman scattering (SERS) spectra of pure and B-doped carbon nanotubes were collected. In simulation approach, using the Gauss View and Gaussian software [basis set 6-31G, computational method DFT (B3LYP)], the spontaneous and SERS spectroscopy of pure and B-doped carbon nanotubes was calculated. Due to the presence of silver nanoparticles in the vicinity of carbon nanotube and boron element, SERS intensity to spontaneous Raman (NR) intensity ratio I SERS = I NR increases in the D, G and boron oxide modes of up to 12-fold were observed. A good agreement is found between the computational and the experimental SERS results for the vibrational spectra of the synthesized composite materials.

In this study, the Raman and the surface-enhanced Raman scattering (SERS) spectra of TiO2 adsorbed on gold/graphene cluster is explained by density functional theory (DFT) calculations. we concentrated on the interaction between TiO2, Au, and graphene, in which graphene is presented as a substrate component in SERS. Results indicate that changing graphene type including pure graphene and B/N-doped graphene enables modifications of interaction between molecule, gold, and graphene cluster. The Raman and SERS spectra of compounds are compared considering the intensity of spectra, which demonstrate the intensity dependence on graphene type which is due to the effects of chemical and electromagnetic properties.

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