The statistical model of crystal melting represents BPS configurations D-branes on a toric Calabi-Yau three-fold. Recently it has been noticed that an infinite-dimensional algebra, the quiver Yangian, acts consistently crystal-melting configurations. We physically derive algebra and its action states, starting with effective supersymmetric quantum mechanics D-brane worldvolume. This leads to re...

If a wave function is written in polar form it becomes possible to write the Schr\"odinger equation of nonrelativistic quantum mechanics analogous classical Hamilton-Jacobi with an extra term known as potential. Time-dependent supersymmetry procedure for finding new solutions if one solution known. In this paper time-dependent transformation applied and shown that potential plus conserved quant...

In particular, there have been studies within Supersymmetric Quantum Mechanics formalism. Cooper et al, [6], for instance, investigated the relationship between shape invariance and exactly analytical solvable potentials and showed that the Natanzon potential is not shape invariant although it has analytical solutions for the associated Schr odinger equation. L evai et al, [7], have determined...