Unformatted text preview: ( ) x p Φ . Now con-sider the eigenvalue problem for position states in the momentum representation, ˆ ( ) ( ) x x x p x p Φ = Φ . Show that this eigenvalue relation is satisfied if the position operator has the form ˆ x i p ∂ = ∂ h . Further, by operating on an arbitrary wavefunction ( ) p ψ , show that this choice produces the fa-miliar result for the position-momentum commutator, ˆ ˆ [ , ] x p i = h ....
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- Fall '08
- momentum operator, position operator, momentum eigenfunctions, Nancy Makri