An approximate solution of the radial Schr€ odinger equation is obtained with a generalized group of potentials in the presence of both magnetic field and potential effect using supersymmetric quantum mechanics and shape invariance methodology. The energy bandgap of the generalized group of potentials was calculated for s À wave cases at the ground state. By varying the numerical values of the potential strengths, the energy band gap of Hellmann's potential and Coulomb-Hulthẻn potential respectively were obtained. It is noted that the inclusion of the potential effect greatly affects the accuracy of the results. Our calculated results are in agreement and better than the existing calculated results. The present results approximately coincide with the standard bandgap of Cu 2 ZnSnS 4 (CZTS).

Nanostructured SnO2 thin films were grown by the chemical spray pyrolysis (CSP) method. Homemade spray pyrolysis technique is employed to prepare thin films. SnO2 is wide band gap semiconductor material whose film is deposited on glass substrate. A gold nanoparticle-doped tin oxide thin film (AuTO) was also prepared. UV-VIS (ultraviolet visible) spectroscopy and four-point probe analysis are done for optical and electrical analysis. UV-Visible absorption spectra show that the band gap of SnO2 thin film is 3.78 eV and 3.82 eV for AuTO. Band gap of SnO2 thin film can be tuned that it can be used in optical devices. The films have transmittance increases (to about 60%) and the absorbance decreases in the visible region of the electromagnetic spectrum. The electrical conductivity of the Tin Oxide is enhanced by functionalizing with the Gold nanoparticles. It is higher than that of the Tin oxide only; 0.77 x 10-2 (Ohm cm)-1 and 3.55 x 10-2 (Ohm cm)-1 for SnO2 and AuTO respectively. These properties reveal that Tin Oxide doped with gold can actually be a good material for a transparent conducting oxide to be used in photovoltaic fabrication and in electronics.