Question: Orthogonal Symbols

I would like to declare spin states; spin up (alpha) and spin down (beta)

such that they form an orthogonal basis not necessarily using Dirac Ket notaion.  I am using the Physics package and Linear Algebra

When I try to use the Dirac Ket notation, I have noncommuting issues with the Cartesian basis

Cart := Vector[column](3, [Ket(X), Ket(Y), Ket(Z)]);

Spin := Vector[column](2, [Ket(alpha), Ket(beta)]);

"Error, (in Check) found more than 1 noncommutative object in the commutative product: -(1/2)*Bra(alpha)*2^(1/2)*(-Bra(X)+I*Bra(Y))"

However, when I choose not to represent the spin states in Ket notation, Maple leaves the inner products in  explicit form rather than evaluating them as alpha.alpha = 1, alpha.beta = 0 etc even if I try to pre-define the expressions.

Many Thanks



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