SLIDE 16 ❉❡✈❡❧♦♣✐♥❣ t❤❡ ▼♦❞❡❧ ▼✐❝r♦♣♦❧✐t✐❝❛❧ ❢♦✉♥❞❛t✐♦♥s ❢♦r θ
❇❛r❣❛✐♥✐♥❣ ♦✉t❝♦♠❡
❇❛r❣❛✐♥✐♥❣ ♣r♦t♦❝♦❧✿
◮ ❖♥❡✲r♦✉♥❞✱ ❝❧♦s❡❞✲r✉❧❡✿ ✐♥❝✉♠❜❡♥t✬s r❡♣r❡s❡♥t❛t✐♦♥ ♦✛❡rs r ❖
s ≤ ✷③s✳
◮ ❖♣♣♦s✐t✐♦♥ ❝❤♦♦s❡s t♦ r❡❥❡❝t ♦r ❛❝❝❡♣t✳ ◮ ■❢ r❡❥❡❝ts✱ ♦♣♣♦s✐t✐♦♥ ❣❡ts✿ r ❖
s =
s = Ψ (ℓ) ✷③s
✇✳♣r✳ Ω (✐, ℓ) ✵ ✇✳♣r✳ ✶ − Ω (✐, ℓ)
❙♦❧✈✐♥❣ ❜❛❝❦✇❛r❞✿
◮ ♦♣♣♦s✐t✐♦♥ ✇✐❧❧ ❛❝❝❡♣t r ❖
s
❛t st❛❣❡ ✷ ♦♥❧② ❛s ❧♦♥❣ ❛s✿ r ❖
s ≥ Ω (✐, ℓ) Ψ (ℓ) ✷③s .
◮ ♦♣t✐♠❛❧ ❢♦r ✐♥❝✉♠❜❡♥t t♦ ♦✛❡r r ❖
s = ✷Ω (✐, ℓ) Ψ (ℓ) ③s = ✷θ (✐, ℓ) ③s✳
◮ ❞❡✜♥❡ θ (✐, ℓ) Ω (✐, ℓ) Ψ (ℓ)✱
θ ✐s t❤❡ ♣r♦❞✉❝t ♦❢ t❤❡ ❜❛r❣❛✐♥✐♥❣ ♣♦✇❡r ♦❢ t❤❡ ♦♣♣♦s✐t✐♦♥ ✭Ω(✐, ❧)✮ ❛♥❞ ♦♣♣♦s✐t✐♦♥✬s st❛t✉s q✉♦ ♦✉t❝♦♠❡ ✭Ψ(❧)✮✳
❚❤❡ ❝❤♦✐❝❡ ♦❢ ♣♦❧✐❝② ✐♥ st❛❣❡ ✶ ✐s ❛s ❜❡❢♦r❡✳
❇❡s❧❡② ✫ P❡rss♦♥ ✭▲❙❊ ✫ ■■❊❙✮ ❈❤❛♣t❡r ✼✿ P♦❧✐t✐❝❛❧ ❘❡❢♦r♠ ❙❡♣t❡♠❜❡r ✷✻✱ ✷✵✶✶ ✶✻ ✴ ✷✽