Study of Schrodinger equation from supersymmetric quantum mechanics

Abstract

Schrodinger equation has a fundamental rule in quantum study. The Supersymmetric Quantum Mechanics formalism is a very useful theoretical tool in the analysis of this equation. This project intent to develop the supersymmetric formalism applied to Quantum Mechanics and to explore the applications of this formalism in the study of quantum systems. In special, we intent to discuss the conjecture that all the exactly solvable quantum potentials have a Hamiltonian hierarchy associate. A possible contra-example for this conjecture can be found by the system composed by the one-dimensional finite square well potential. On the other hand, an equation, similar to Schrodinger one, has been used to describe the properties of lattices which modeling the DNA macromolecule. In this way, the super-algebra approach can contribute to compute important information for this system, as the melting temperature. One model including the vibrations and rotations motions of the bases pairs in the same formalism will be studied and the physical implications will be discuss. (AU)