Parasupersymmetry and Shape Invariance in Differential Equations of Mathematical Physics and Quantum Mechanics

It has been shown that all second-order associated differential equations obtained from the master function have the properties of parasupersymmetry and shape invariance. Using this fact, all of the well-known one-dimensional shape invariant parasupersymmetric Hamiltonians have been obtained by an appropriate choice of master function and corresponding weight function, where only two of these parasupersymmetric Hamiltonians can be interpreted as the Hamiltonian of motion of spin-(p/2) particle in the presence of a magnetic field along thez-axis.