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2. (10 pt) Let $|l, m\rangle$ represent angular momentum states with integer $l$ and the radial quantum number omitted. (a) Show that $\langle l, m'|z|l, m\rangle = 0$, $\langle l, m'|p_z|l, m\rangle = 0$ by using the parity-selection rule. (b) Show that $\langle l+2, m'|z|l, m\rangle = 0$, $\langle l+2, m'|p_z|l, m\rangle = 0$ by using the parity-selection rule. (Note: recall that you made the same conclusions in the previous homework with the Wigner-Eckart theorem.) (c) Show that $\langle l+1, m'|z^2|l, m\rangle = 0$, $\langle l+1, m'|p_z^2|l, m\rangle = 0$, $\langle l+1, m'|\{z, p_z\}|l, m\rangle = 0$ by using the parity-selection rule.

          2. (10 pt) Let $|l, m\rangle$ represent angular momentum states with integer $l$ and the radial quantum number omitted.
(a) Show that $\langle l, m'|z|l, m\rangle = 0$, $\langle l, m'|p_z|l, m\rangle = 0$ by using the parity-selection rule.
(b) Show that $\langle l+2, m'|z|l, m\rangle = 0$, $\langle l+2, m'|p_z|l, m\rangle = 0$ by using the parity-selection rule.
(Note: recall that you made the same conclusions in the previous homework with the Wigner-Eckart theorem.)
(c) Show that $\langle l+1, m'|z^2|l, m\rangle = 0$, $\langle l+1, m'|p_z^2|l, m\rangle = 0$, $\langle l+1, m'|\{z, p_z\}|l, m\rangle = 0$ by using the parity-selection rule.

$2. (10 pt) Let |l, m⟩ represent angular momentum states with integer l and the radial quantum number omitted. (a) Show that ⟨ l, m'|z|l, m⟩ = 0, ⟨ l, m'|pz|l, m⟩ = 0 by using the parity-selection rule. (b) Show that ⟨ l+2, m'|z|l, m⟩ = 0, ⟨ l+2, m'|pz|l, m⟩ = 0 by using the parity-selection rule. (Note: recall that you made the same conclusions in the previous homework with the Wigner-Eckart theorem.) (c) Show that ⟨ l+1, m'|z^2|l, m⟩ = 0, ⟨ l+1, m'|pz^2|l, m⟩ = 0, ⟨ l+1, m'|{z, pz}|l, m⟩ = 0 by using the parity-selection rule.$

Added by Esperanza L.

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