Quantum Mechanics: Concepts and Applications · Problem 2.3

Mathematical Tools of Quantum Mechanics — Nouredine Zettili

Physics — Quantum Mechanics · bra-ket-algebra

Problem

Consider the following two kets: ∣ψ⟩=(−3i2+i4),∣ϕ⟩=(2−i2−3i)|\psi\rangle = \begin{pmatrix} -3i \\ 2+i \\ 4 \end{pmatrix}, \qquad |\phi\rangle = \begin{pmatrix} 2 \\ -i \\ 2-3i \end{pmatrix} (a) Find the bra ⟨ϕ∣\langle \phi |. (b) Evaluate the scalar product ⟨ϕ∣ψ⟩\langle \phi | \psi \rangle. (c) Examine why the products ∣ψ⟩∣ϕ⟩|\psi\rangle|\phi\rangle and ⟨ϕ∣⟨ψ∣\langle\phi|\langle\psi| do not make sense.

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