By Pratt S.
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II.
II.
Q❯✤✯✘✙✛rts❃✉✲s✇✈①◗✭❝✏❯✤✯✘✙❲❤✪✜✤◗✪✗✶❙✘✖✐❚②❯✰✦✭❯✤✙◆✵ ❦④③ ❧❫⑤⑥❝❆❯✤✯✘✙❱✦✭❯✤◗✪❥⑦✣❬❚✏✣❬❙⑧✦❥⑨✦◆❤✪❙✶✙❭❯✡✣✥✮❶⑩✘✙❍❩❬✖❷◗◆❝❆❸✶✵❹❸✶✱q❺✟✙❍❚✤❩❬✦✶✩◆⑩✢❙✶✖❻❯✡✯✘✙q❥⑨✦◆❤✪❙✶✙❭❯✡✣✥✮❉✙❭❙✘✙❍✜❜❤✪✣❬✙❭❚❼◗◆❝☎❯✡✯✶✙❘◗✪✜❜✣❬❤✪✣✥❙✢✦◆❩❬❩❽✧ ✖✘✙❍❤✪✙❭❙✘✙❍✜✤✦✭❯✡✙❷❾❣✈⑨❿♣✱✛❚②❯✰✦✭❯✤✙❍❚❭✵ ❾❣✵➀➁❙✘✙❷✙❍❩❬✙❭✮❭❯✤✜✤◗✪❙❏❥❁◗✴➂✪✙❍❚✣❬❙❏✦❋◗✪❙✶✙➃❵❨✖✶✣❬❥❁✙❍❙✘❚❜✣❬◗✪❙✢✦✭❩✟❚②✧❣❚❜❯✡✙❭❥➄✦◆❙✘✖✽❝④✙❭✙❍❩✟❯✡✯✘✙❻✣✥❙♠❯✡✙❍✜✤✦◆✮❭❯✤✣❬◗✪❙✬◗◆❝➅❯❨❳❘◗✻✦✭❯✤◗✪❥❁❚❍✵➁➆✝❴❛❵ ❴✶✜✤◗★❢❛✣❬❥⑨✦✭❯✡✙❯✤✯✘✙❲✣❬❙♠❯✡✙❭✜✡✦◆✮➃❯✡✣✥◗✪❙ ③ ✙➃❯❨❳❘✙❭✙❍❙✐❯✤✯✘✙❲✙❍❩✥✙❍✮❭❯✤✜✤◗✪❙✶❚✝✦✭❙✘✖✻❯✤✯✘✙✛✦✭❯✡◗◆❥⑨❚q❳❪✣❽❯✡✯❫❯✡✯✘✙❲❴❆◗◆❯✡✙❭❙♠❯✡✣➇✦✭❩ ➈ ❦④➉ s➋➊❲❧➍➌➎s✕➏✏➐ ❦④➉ s❃➊❲❧➃➑ ❳❪✯✶✙❍✜✤✙✛➊➒✣❬❚q❯✡✯✶✙✛❴❆◗✪❚❜✣✥❯✡✣✥◗✪❙❫◗◆❝❞✦◆❙✐✦✭❯✡◗✪❥✻✵➅➓✕❚✤✙➔❯✡✯✘✙✛✦◆✖✶✣➇✦ ③ ✦→❯✡✣❬✮➁✦◆❴✘❴✘✜❜◗✴❢❛✣✥❥♦✦✭❯✤✣❬◗✪❙⑨❯✡◗ ❦ ✦♠❧✍➣❲✣❽➂✪✙❍❙❲❯✡✯✶✙➍❯❨❳❉◗✝✦✭❯✡◗✪❥❁❚❡✦◆✜❜✙➍❚✤✙❍❴✘✦◆✜✡✦✭❯✤✙❍✖ ③ ✧✛✦❪✖✶✣❬❚❜❯✡✦◆❙✘✮❭✙❶↔❣✩✴⑩✢❙✘✖✹✦q❯✡✜✡✦✭❙✘❚✤✮❭✙❍❙✘✖✘✙❭❙♠❯✰✦◆❩↕✙❍➙↕✗✢✦→❯✡✣❬◗◆❙✹✜❜✙❍❩➇✦→❯✡✣❬❙✶❤ ➛✻✦◆❙✶✖✐↔❷❳❪✯✶✙❍✜✤✙❲❯✡✯✶✙✛✙❭❩❬✙❭✮❭❯✡✜❜◗✪❙✘✣✥✮ ③ ✣❬❙✘✖✶✣❬❙✘❤⑧✙❭❙✘✙❍✜❜❤◆✧❫✣❬❚➁➝☎➜ ➞➟➛ ➞➃➠ ❦ ❾✭➡✻❧➟✵ ❦④③ ❧✍✚❞✣❬❙✘✖❫❯✤✯✘✙❲❴➢◗◆❯✤✙❍❙♠❯✡✣❬✦◆❩ ③ ✙❭❯❨❳❉✙❍✙❭❙✐❯✡✯✶✙❲❯❨❳❉◗❋✦→❯✡◗✪❥❁❚❱✦✭❯✕❚✤❥⑨✦◆❩✥❩✿↔❣✩ ➈ ❦ ↔❲➤ ❸♠❧➍➥ ➈ ❦ ↔✛➌➦❸♠❧❞s❃➧✟↔➨➑ ❯✡✯✢✦✭❯❉✣❬❚❭✩♠⑩✢❙✘✖ ➈ ❦ ↔❲➌➩❸✪❧➍✦✭❙✘✖❋➧❶✵➅➫➁◗✛❯✤✯✘✣❬❚ ③ ✧❁✙➃❢❛❴✢✦◆❙✶✖✘✣❬❙✘❤✛❯✡✯✘✙❪❯✡✜✤✦◆❙✘❚❜✮❍✙❍❙✶✖✘✙❍❙♠❯✰✦✭❩✿✙❍➙↕✗✢✦→❯✡✣❬◗◆❙♦✣❬❙➭❯✡✙❭✜✤❥❁❚ ◗◆❝↔❣✵❃➯✝✣✥❙♠❯★➲✍✚❞✣✥✜✤❚❜❯❍✩❶⑩✘❙✘✖ ➈ ❦ ↔➳➌➄❸♠❧ ③ ✧❃❚✤◗✪❩❽➂❣✣❬❙✘❤✽❯✤✯✘✙❫❯✡✜✡✦✭❙✘❚✤✮❭✙❍❙✘✖✘✙❭❙♠❯✰✦◆❩✕✙❍➙↕✗✢✦✭❯✤✣❬◗✪❙➋❳❪✣❽❯✡✯❃↔➳➌➵❸❛✵ ❺❞✦◆➸✭✙➭✖✘✙❍✜❜✣✥➂✭✦✭❯✡✣❽➂✪✙❭❚➁◗◆❝➅❯✡✯✶✙❻❯✡✜✡✦✭❙✘❚✤✮❭✙❍❙✘✖✘✙❭❙♠❯✰✦◆❩➅✙❭➙❣✗✘✦✭❯✡✣✥◗✪❙✽❳❪✣✥❯✤✯✽✜✤✙❭❚✤❴❆✙❍✮❭❯❲❯✤◗❋↔❛✩➢❯✡✯✘✙❭❙✲❚❜◗✪❩✥➂◆✙❷❝④◗✪✜➔➺❣➛ ➠ ➺↕↔ ✦✭❯❪↔✛➌➦❸✶✩☎✦✭❙✘✖❫⑩✢❙✢✦◆❩✥❩✥✧♦⑩✘❙✘✖✬➺↕➻ ➠ ➺♠↔✹❯✡◗❁◗ ③ ❯✡✦◆✣❬❙✍➧❶✵ ❦ ✮✴❧✍✚❞✣❬❙✘✖❫❯✤✯✘✙❲❴➢◗◆❯✤✙❍❙♠❯✡✣❬✦◆❩ ③ ✙❭❯❨❳❉✙❍✙❭❙✐❯✡✯✶✙❲❯❨❳❉◗❋✦→❯✡◗✪❥❁❚❱✦✭❯✕❩➇✦✭✜✤❤✪✙➁↔❣✩ ➈ ❦ ↔❲➤ ➼➽❧❶➌⑦s✕➾✙➃❢❛❴ ❦ s❾✪➛♠➚➁↔◆❧➃➑ ❯✡✯✢✦✭❯❼✣❬❚❍✩→⑩✢❙✘✖⑧➾✟✵❼➯✕✣❬❙♠❯★➲✏➓✝❚❜✙❘⑩✢✜✤❚②❯➅◗✪✜❜✖✘✙❍✜❼❴❆✙❍✜②❯✡✗✘✜ ③ ✦✭❯✤✣❬◗✪❙❷❯✤✯✘✙❍◗◆✜❜✧✪✩↕✦✭❚✤❚✤✗✶❥⑨✣✥❙✘❤❯✡✯✶✙q✗✘❙✘❴❆✙❍✜②❯✡✗✘✜ ③ ✙❭✖➭❳❘✦★➂✪✙ ❝④✗✘❙✘✮❭❯✤✣❬◗✪❙✍✣✥❚q❯✡✯✘✙ ③ ◗✪✗✘❙✘✖✻❚❜❯✡✦✭❯✡✙❲◗◆❝✟◗✪❙✶✙❲❳❉✙❍❩✥❩➪✩✶✦◆❙✘✖✍❯✡✯✘✙➔❴❆✙❍✜②❯✡✗✘✜ ③ ✦✭❯✡✣✥◗✪❙✍✣❬❚q❯✤✯✘✙➔✣❬❙♠❯✡✙❭✜✡✦◆✮➃❯✡✣✥◗✪❙❋❳❪✣✥❯✤✯✍❯✤✯✘✙ ❚✤✙❍✮❭◗✪❙✘✖✻❳❘✙❭❩❬❩➪✵ ✂✁☎✄✝✆✟✞✡✠☞☛ ✌✍✠✏✎✒✑✔✓✝✕ ✖✘✗✘✙✛✚✢✜✤✣✥✖✢✦★✧✪✩☎✫✬✦✭✜✤✮✰✯✬✱✳✲✵✴ ✶✸✷✺✹✼✻✾✽❀✿❁✻❃❂☎❄❆❅❈❇❉✻✾✶✛❊❋✽❍●❏■❑❅✢▲☎▲✟▼ ◆ ✴❖◗✯✘❘❀❙❯❚✡✯✢✦❱❚❳❲❩❨ ❬✳❭✢❪❫❬❵❴✪❨ ❴❩❛❝❜ ❘✳✜❉✦✸❞❡❘◗❘✪❢❣❴ ✙❤✜✐❢✢✦✳✣❥✜❦❙❧✣♠❚✡✯♦♥q♣srt✣❥✉❉✈s✴❦✇①✉✤✙✝❚✤✯✘✙ ❜ ✦✳✮❤❚✐❚✤✯✢✦✭❚✐❚✡✯✘✙❧❙❡✦❀②✳✙ ❜ ✗✘③✵✮❤❚✡✣✥❘✪③ ④ ❘⑤✙❤✉❧✦✳✉✸⑥⑦✮❍❘✳✉❵⑥⑨⑧❶⑩★❷✳❸✏❪❹✮❍❘✪✉❀⑥⑨⑧✪❺❩❷✪❸❻❸✘❼✭❷ ✦❱❚✝❽❥✦✳✜ ④ ✙❳❷⑤✴ ✂✁☎✄✝✆✟✞✡✠☞☛ ✌✍✠✏✎✒✑✔✓✖✕ ✗✙✘✙✚✜✛✣✢✥✤✦✗✣✧✩★✫✪☎✬✭✧✮✢✥✯✱✰✳✲✫✴✶✵ ✷✹✸✻✺✽✼✿✾❁❀❂✼❄❃☎❅❇❆❉❈❊✼✿✷✜❋●✾■❍❑❏▲❆✣▼☎▼✟◆ ❖ ✵◗❙❘❯❚✙❱✥✤✦✗✙✚■✢❲✧❨❳✣✧❯✢❬❩✡✤❭✯❫❪❭✚❴❘✮❵❜❛❝✧❯❱✥❱❡❞❢✧❯❚✙✗✍✯✱✰✣✧❯✢❤❣✫✚❥✐❦❛❂❘♠❧♥✤✦❚✙❣♦✤❭❚●❩✡✰✶✚❦♣rqtsr❳✙❪❭✧❯❚✙✚✉✘✙❚✶✗✙✚■✢❡❩✡✰✙✚❦✤✦❚✶✈✣✘✙✚❫❚✙✯■✚❦❘❯❵ ✧❨❛❝✧❯❣✫❚✙✚✇❩✡✤✦✯◗①✣✚■❪✦✗✳✤✦❚●❩✡✰✙✚✜②❂✗✙✤❭✢❤✚■✯❫❩✥✤❭❘✫❚✿✵④③⑤❣✫❚✙❘✫✢❤✚❦❛❝❘❯❩✥✤❭❘✫❚r✤❭❚⑥❩✡✰✙✚✜②♦✗✙✤❭✢❤✚■✯✇❩✡✤❭❘❯❚❉✵ ⑦ ✧⑨⑧✍⑩❶✰✙❘❁❷❸❩✡✰✙✧✮❩❹❩✡✰✙✚✉❧❯✚■✯❫❩✥❘✫✢❲❳❺❘❯❩✥✚■❚⑨❩✡✤❭✧❯❪❻✪ ❼❾❽➀❿ ➁ ⑦ ♣❡s➃➂ qts➄♣❇➂ ⑧✿➅ ✗✙✚■❱❤✯■✢✥✤✦➆❺✚❫❱◗✧❨❛❝✧❯❣✫❚✙✚✇❩✡✤✦✯❴①✣✚■❪✦✗✻✤✦❚⑥❩✡✰✙✚✜②♦✗✙✤❭✢❤✚■✯❫❩✥✤❭❘✫❚✿✵ ⑦ ➆☎⑧✍➇④➈❶❳✙✢❤✚■❱❤❱❲❩✥✰✙✚✉❧✫✚■✯✇❩✡❘✫✢❡❳❇❘❯❩✡✚❫❚⑨❩✡✤➉✧✮❪✿✤❭❚⑥✯✇★♥❪❭✤❭❚✶✗✙✢✥✤✦✯✩✧❯❪❺✯■❘♥❘✫✢✥✗✙✤✦❚✣✧✮❩✥✚■❱■✪♥❩✡✰✣✧➊❩❡✤❭❱➋✤✦❚✍❩✥✚■✢❤❛❝❱➋❘✮❵❜➌♥✪☎➍✟✪➄➌❨➂ ✧❯❚✙✗ ➍☞➂ ✵ ⑦ ✯❁⑧●➎➏✢❤✤✦❩✡✚❴❩✥✰✙✚✹⑩❶✯✱✰✙✢✩❘✫➐ ✗✙✤❭❚✶❣✫✚■✢❡✚■➑➒✘✣✧➊❩✡✤❭❘❯❚❉✪ ⑦➔➓ qt➁ ✐❁❼✍→❯➣❫⑧❬↔ ⑦ ➌♠➅➙➍❺⑧➛❽➝➜ ⑦ ➌♠➅➙➍❺⑧✇➅ ⑦❖⑧ ❞ ↕ ↕ ✤❭❚✍✯❫★♥❪❭✤✦❚✙✗✙✢❤✤❭✯✩✧✮❪✿✯■❘♥❘✫✢❤✗✙✤❭❚✣✧➊❩✡✚■❱❫✵ ⑦ ✗☎⑧✻⑩❶✰✙❘❁❷❸❩✡✰✙✧✮❩❲➞➛➟◗✯■❘❯❛❝❛➃✘❶❩✡✚■❱➋❷❡✤➠❩✡✰⑥❩✡✰✶✚✹➡✝✧❯❛❂✤❭❪✦❩✥❘✫❚✙✤❭✧❯❚❉✵ ⑦ ✚❁⑧⑥➢◗❱✥❱❤✘✙❛❂✤❭❚✙❣❨❩✡✰✶✚✜❱❤❘✫❪❭✘❶❩✡✤❭❘❯❚⑥✤❭❱❲✧❯❚✍✚■✤✦❣✫✚■❚✙❱❬❩✱✧✮❩✥✚❦❘❯❵④➞➛➟❲❷❡✤✦❩✡✰✍✚❫✤❭❣✫✚❫❚➒❧✮✧❯❪✦✘✙✚✉❞✽➥❉➤ ✪ ↕ ⑦ ➌♠➅➙➍✿⑧➄❽➦✐■➧➩➨❜➫♠➭ ➨ ⑦ ➌❯⑧✇➅ ✢✥✚❫❷❡✢❤✤✦❩✥✚❦❩✥✰✙✚✹⑩❶✯✱✰✙✢✩❘✫➐ ✗✙✤❭❚✶❣✫✚■✢❡✚■➑➒✘✣✧➊❩✡✤❭❘❯❚✍❵➔❘❯✢➋➭ ➨ ⑦ ➌❯⑧✇✵ ⑦ ❵✡⑧●➯◗➲❉➳❁➵♠➸ ❀ ➵➊➺♥➻✟➼➔➳✫➽➄⑩❶❘✫❪➠❧✫✚✉❵➔❘✫✢➋❩✡✰✶✚❦➭ ➨ ⑦ ➌❯⑧➋✧❯❚✙✗✍❩✡✰✙✚❦✚■✤✦❣✫✚■❚✶✚■❚✙✚❫✢✥❣✫✤✦✚■❱❹❵➔❘✫✢➋❩✡✰✶✚✜✯■✧❯❱✥✚❦❷❡✰✙✚❫✢✥✚❦❞➾❽➝✴❶✵ ➁ ✵◗❙❘❯❚✙❱✥✤✦✗✙✚■✢r✧➚✯✱✰✣✧❯✢❤❣✫✚■✗➪✢❤✚■❪❭✧✮❩✡✤➠❧❶✤✦❱❤❩✥✤❭✯⑥❳✣✧❯✢❬❩✡✤✦✯■❪❭✚✻✤❭❚⑨❩✥✚■✢✡✧✮✯❫❩✡✤✦❚✙❣➶❷❡✤✦❩✡✰✂❩✡✰✙✚✳✚■❪❭✚❫✯❫❩✥✢✥❘✫❛❝✧❯❣✫❚✙✚✇❩✡✤✦✯✍①✙✚■❪❭✗✿✪❡✧❯❚✙✗➹✗✙✚➙➘ ❱❤✯■✢❤✤❭➆❇✚■✗✍➆⑨★⑥❩✡✰✙✚✜➴✉❪❭✚❫✤❭❚❶➘➬➷❦❘✫✢❤✗✙❘✫❚●✚❫➑➒✘✣✧✮❩✡✤✦❘✫❚❉✵ ➮ ⑦✃➱ ➥❇➤ ❐✫❒❺q❄✐♠❮❹⑧ ↔❜❰ ➣ ↔ ➥➤ ↔ ❐ Ï↔ qt❞ ↔ ➣✱Ð✥Ñ ⑦ ♣☞➅✥Ò❤⑧➄❽➦✴ ↕ Ó ✰✶✚✜✚❫❪❭✚❫✯❫❩✡✢❤❘✫❱❤❩✡✧✮❩✡✤✦✯✉❳❺❘✮❩✡✚■❚⑨❩✥✤➉✧❯❪☞❮Ô✤❭❱❹✤✦❪❭❪❭✘✶❱❤❩✡✢✥✧✮❩✡✚❫✗⑥✤❭❚●❩✥✰✙✚❦✗✙✤➉✧❯❣❯✢✡✧❯❛❾➆❺✚❫❪❭❘❁❷❦✵ E-mc 2 I.
Quantum mechanics. Problem Set by Pratt S.
by Kenneth
4.4