The Shape Invariance in <Emphasis Type="Italic">S</Emphasis><Superscript>2</Superscript> Space with Electromagnetic Field

In this paper, we use the Laplace equation in curvature space S ² with electromagnetic field, and write the Schrödinger equation in S ²space. By comparing this equation with well known polynomial we obtain the wave function and energy spectrum. In that case we face with two values of λ which guarantee the stability of system. On the other hand, we take advantage from factorization method, and factorize the second order equation in terms of first order equations. These first orders operators lead us to investigate the potential and super-potential which are satisfied by shape invariance condition. We show that, in order to have such condition the λ must be zero, the energy spectrum also obtained by this condition. Finally we show that these corresponding operators will be generators of algebra.     

Montmorillonite K10: an effective catalyst for synthesis of 2-aminothiazoles

Research on Chemical Intermediates - An efficient one-pot synthesis of 2-aminothiazoles from methylcarbonyl and thiourea has been developed using montmorillonite-K10 as a catalyst at...     

Fe3O4@MCM-48-SO3H:An efficient magnetically separable nanocatalyst for the synthesis of benzo[f]chromeno[2,3-d]pyrimidinones

Sulfonic acid groups were grafted onto three different types of synthesized magnetic nanoparticles, namely Fe3O4, Fe3O4@SiO2, and Fe3O4@MCM‐48. The sulfonic acid‐functionalized nanoparticles were evalu...