Supersimmetria in meccanica quantistica

Supersymmetry (SUSY) was originally introduced to obtain a unifed description of forces and matter. It relates bosonic and fermionic degrees of freedom and provides a more elegant description of nature. Supersymmetric quantum mechanics (SUSYQM) emerged as a byproduct of supersymmetric quantum field theories, but it was soon clear was an interesting topic on its own because of its moltidude of aspects. The first application of SUSYQM is to find solutions of tricky Schr\"odinger equations. SUSY partner potentials have degenerate spectra, except for one state if SUSY is exact. Then one can build an entire class of potentials which have the same shape of their partner (SIP). The first property of SIP is that it's possibile to reconstruct the full spectrum by just knowing the ground state. During the study of continuum spectra, SUSY formalism (how changes the number of nodes in degeneracy levels) became a study of the number of singularity points in reflection and transmission coefficients. Then SUSYQM it's useful also in WKB approximation (SWKB) because it gives the exact spectra for SIP. Also there are some relations between PTC and SIP. These aren't all the applications of SUSYQM. Otherwise this is just an introduction. In an advanced article one could study SUSYQM in a more general way, finding more aspects all of these applications have in common.