Introducing Quantum Information with the Quadratic Equation

From Pauli's exclusion principle, a given state can be occupied by either zero or one fermion or n² = n, a quadratic equation with solutions of 0 and 1. Pure density matrices satisfy the same equation. This implies a method of teaching quantum mechanics appropriate for early college students: generalize the quadratic equation to symmetry groups. This allows students to understand elements of quantum mechanics without the complications of partial differential equations, and it also suggests a new method of understanding the Standard Model.