Simetrías en la naturaleza y efecto túnel: breve estudio de pozos cuánticos dobles

Abstract

It is interesting to understand the mechanism by which some materials in nature, with an asymmetrical appearance, are formed and to relate it with a quantum problem. For this reason, we analyze with full details the behavior of a quantum particle in a finite double well potential and in a similar one, a double Dirac delta function well in order to explain, how and when, the symmetry breakup takes place in these cases. For simplicity we consider both potentials in one dimension ($x$) and we focus our attention on the symmetry $V(x)=V(-x)$ of the potentials. We find, and illustrate in detail, the eigenstates (and energies) of the Hamiltonian $\hat{H}$ and of the parity symmetry $\hat{\pi}$ operator. We determine the time evolution of the parity-eigenstates, we find that the parity symmetry is broken when they are combined in a special way and we set out the consequences of this breaking. We emphasize the relevance of the tunnel effect which arises in the quantum treatment of the problems and we relate the obtained results with naturally occurring situations and materials (NH$_3$), its possible influence on our environment and particularly, with the physics involved in the operation of the Maser.