Question

Let α and β be possible quantum states of a quantum system, while Aˆ is an operator in its Hilbert space. Which of the following expressions are allowed in the bra-ket formalism?

(a) <α>; (b) <α|β>^2; (c) |α><β|; (d) <Aˆ>; (e) <α|Aˆ; (f) |α>|β>; (g) |α>^2 ; (h) A^ˆ2 ; (i) Trace (|α><β|).

For each meaningful expression, state whether it is a vector, an operator, or a scalar. If (i) is meaningful, evaluate it (using matrix representation).

Answer 1