PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Quantum Mechanics · The formalism of quantum mechanics
The Structure of Quantum Mechanics, Ch Hilbert space and Dirac notation
Problem
A spin-1/2 state is written ∣χ⟩=(1+i)∣↑⟩−2i∣↓⟩ in the Sz basis, where ⟨↑∣↑⟩=⟨↓∣↓⟩=1 and ⟨↑∣↓⟩=0.
((a)) Write the bra ⟨χ∣.
((b)) Compute ⟨χ∣χ⟩.
((c)) Repeat (b) with the coefficients left unconjugated, as if the bra correspondence were linear, and say why the result cannot be a squared length.