Hückel Theory

Ethene

A={{α-ε,β},{β,α-ε}}

Solve[Det[A]==0,ε]

eqn=A.{c1,c2}==0

ε=α+β

Solve[eqn,{c1,c2}]

ε=α-β

Solve[eqn,{c1,c2}]

1,3-Butadiene

ε=.

A={{α-ε,β,0,0},{β,α-ε,β,0},{0,β,α-ε,β},{0,0,β,α-ε}}

MatrixForm[A]

sol=Solve[Det[A]==0,ε]

sol[1]

N[Expand[sol],10]

eqn=A.{c1,c2,c3,c4}==0

ε=ε /. sol[[4]]

ε

Solve[eqn,{c1,c2,c3,c4}]

N[%,10]

ε=ε /. sol[[3]]

Solve[eqn,{c1,c2,c3,c4}]

N[%]