# Symmetric double square well

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*2020-02-20 13:20*

Symmetric finite square double potential well. This is how my Potential looks like: Region I ( xIt is possible to derive exact solutions of the Schrdinger equation for an infinite square well containing a finite rectangular barrier, thus creating a doublewell potential. The problem was previously approached using perturbation theory [1. We consider the potential for and, for, symmetric double square well

The symmetric doublewell. One expands around one of the two minima of the potential. In addition this method requires matching of different branches of solutions in domains of overlap. The application of boundary conditions finally yields (as in the case of the periodic potential) the nonperturbative effect.

symmetry breaking transitions, is a quartic function of The square double well potential is shown in red, with the analytic form given by Eq. (1). The quadratic form is shown in blue, and is given by Eq. (2); it has a maximum (cusp) at the value V cusp. The quartic Regarding symmetry: The wavefunctions do not need to have the same symmetry as the potential. Of course if you have a solution wavefunction, then the mirrored wavefunction must be a solution as well (if the potential is symmetric as in your case). It needs to belong to the same energy eigenvalue.**symmetric double square well** Determine the splitting between the lowest two levels of the double square well with positive inversion symmetry. Compare this with the comparable splitting for the potential of Eq. (1), which you can get from the numbers in Table I. Also, calculate the splitting between the positive and