1. The problem statement, all variables and given/known data Solve for the wavefuntions using the Secular Determinant, of cyclopropene anion/cation/whocares. 2. Relevant equations Secular determinant: | x 1 1| | 1 x 1| |1 1 x | 3. The attempt at a solution I'm literally understanding every aspect of this concept, but what I cannot understand is the math behind the solutions. It looks very un-math like, more of an intuitive answer but I want to know how to solve the math out, because quite frankly its making me angry that something so simple is stumping me. Anyway: Solving the matrix yields x = -2,1,1 Psi 1: -2c1 + c2 + c3 = 0 c1 + -2c2 + c3 = 0 c1 + c2 + -2c3 = 0 c1^2 + c2^2 + c3^2 = 1 The solution for the secular polynomial of x=-2 is simple: you can solve it out for c1=c2=c3 and the only solution that satisfies that is c = (√3 /3) My problem now lies with solving for the psi 2 and psi 3 solutions. I know the answers are psi2: c1 = 0 c2 = +√2 / 2 and c3 = - √2 / 2 psi3: c1 = 2/√6 c2 = c3 = -1/√6 I have no idea how the math from this system can solve for those variables. I'm completely missing something here. c1 + c2 + c3 = 0 c1 + c2 + c3 = 0 c1 + c2 + c3 = 0 c1^2 + c2^2 + c3^2 = 1 Thank you.