Ảnh hưởng của sự giam giữ phonon lên cộng hưởng từ phonon trong giếng lượng tử thế tam giác

✣❸■ ❍➴❈ ❍❯➌ ❚❘×❮◆● ✣❸■ ❍➴❈ ❙× P❍❸▼ ◆●❯❨➍◆ ❚❍➚ ❚❍❆◆❍ ❍⑨ ❷◆❍ ❍×Ð◆● ❈Õ❆ ❙Ü ●■❆▼ ●■Ú P❍❖◆❖◆ ▲➊◆ ❈❐◆● ❍×Ð◆● ❚Ø ✲ P❍❖◆❖◆ ❚❘❖◆● ●■➌◆● ▲×Đ◆● ❚Û ❚❍➌ ❱❯➷◆● ●➶❈ ❙❹❯ ❱➷ ❍❸◆ ▲❯❾◆ ❱❿◆ ❚❍❸❈ ❙➒ ❱❾❚ ị ì ứ ✷✵✶✾ ✣❸■ ❍➴❈ ❍❯➌ ❚❘×❮◆● ✣❸■ ❍➴❈ ❙× P❍❸▼ ◆●❯❨➍◆ ❚❍➚ ❚❍❆◆❍ ❍⑨ ❷◆❍ ❍×Ð◆● ❈Õ❆ ❙Ü ●■❆▼ ●■Ú P❍❖◆❖◆ ▲➊◆ ❈❐◆● ❍×Ð◆● ❚Ø ✲ P❍❖◆❖◆ ❚❘❖◆● ●■➌◆● ▲×Đ◆● ❚Û ❚❍➌ ❱❯➷◆● ●➶❈ ❙❹❯ ❱➷ ❍❸◆ ❈❤✉②➯♥ ♥❣➔♥❤✿ ❱❾❚ ▲Þ ▲Þ ❚❍❯❨➌❚ ❱⑨ ❱❾❚ ▲Þ ❚❖⑩◆ ▼➣ sè ✿ ✽ ✹✹✵ ✶✵✸ ▲❯❾◆ ❱❿◆ ❚❍❸❈ ❙➒ ❱❾❚ ▲Þ ❚❍❊❖ ✣➚◆❍ ì ữớ ữợ P ▲➊ ✣➐◆❍ ❚❤ø❛ ❚❤✐➯♥ ❍✉➳✱ ♥➠♠ ✷✵✶✾ ✐ ▲❮■ ❈❆▼ ✣❖❆◆ ❚æ✐ ①✐♥ ❝❛♠ ✤♦❛♥ ✤➙② ❧➔ ❝æ♥❣ tr➻♥❤ ♥❣❤✐➯♥ ❝ù✉ ❝õ❛ r✐➯♥❣ tæ✐✱ ❝→❝ sè ❧✐➺✉ ✈➔ ❦➳t q✉↔ ♥❣❤✐➯♥ ❝ù✉ ♥➯✉ tr♦♥❣ ❧✉➟♥ ✈➠♥ ❧➔ tr✉♥❣ t❤ü❝✱ ✤÷đ❝ ỗ t sỷ ữ tø♥❣ ✤÷đ❝ ❝ỉ♥❣ ❜è tr♦♥❣ ❜➜t ❦ý ♠ët ❝ỉ♥❣ tr➻♥❤ ♥❣❤✐➯♥ ❝ù✉ ♥➔♦ ❦❤→❝✳ ❍✉➳✱ t❤→♥❣ ✾ ♥➠♠ ✷✵✶✾ ❚→❝ ❣✐↔ ❧✉➟♥ ✈➠♥ ◆❣✉②➵♥ ❚❤à ❚❤❛♥❤ ❍➔ ✐✐ ▲❮■ ❈❷▼ ❒◆ ❍♦➔♥ t❤➔♥❤ ❧✉➟♥ ✈➠♥ tèt ♥❣❤✐➺♣ ♥➔②✱ tæ✐ ①✐♥ ❜➔② tä ❧á♥❣ ❜✐➳t ì♥ s➙✉ s➢❝ ✤➳♥ t❤➛② ❣✐→♦ P t t ữợ ✈➔ ❣✐ó♣ ✤ï tỉ✐ tr♦♥❣ s✉èt q✉→ tr➻♥❤ t❤ü❝ ❤✐➺♥ ❧✉➟♥ ✈➠♥ ♥➔②✳ ◗✉❛ ✤➙②✱ tæ✐ ①✐♥ ❝❤➙♥ t❤➔♥❤ ❝↔♠ ỡ qỵ ổ tr t ỵ ♣❤á♥❣ ✣➔♦ t↕♦ ❙❛✉ ✤↕✐ ❤å❝✱ ❚r÷í♥❣ ✣↕✐ ❤å❝ ❙÷ ♣❤↕♠✱ ✣↕✐ ❤å❝ ❍✉➳❀ ❝→❝ ❜↕♥ ❤å❝ ✈✐➯♥ ❝❛♦ ❤å❝ ❦❤â❛ ✷✻ ❝ò♥❣ ❣✐❛ ✤➻♥❤✱ ❜↕♥ ❜➧ ✤➣ ✤ë♥❣ ✈✐➯♥✱ õ ỵ ú ù t tổ tr q✉→ tr➻♥❤ ❤å❝ t➟♣ ✈➔ t❤ü❝ ❤✐➺♥ ❧✉➟♥ ✈➠♥✳ ❍✉➳✱ t❤→♥❣ ✾ ♥➠♠ ✷✵✶✾ ❚→❝ ❣✐↔ ❧✉➟♥ ✈➠♥ ◆❣✉②➵♥ ❚❤à ❚❤❛♥❤ ❍➔ ✐✐✐ ▼Ö❈ ▲Ö❈ ❚r❛♥❣ ❜➻❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ❚r❛♥❣ ♣❤ö ❜➻❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✐ ▲í✐ ❝❛♠ ✤♦❛♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✐✐ ▲í✐ ❝↔♠ ì♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✐✐✐ ▼ö❝ ❧ö❝ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶ ❉❛♥❤ ♠ö❝ ❝→❝ ❤➻♥❤ ✈➔ ỗ t ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷ ✶✳✶✳ ❚ê♥❣ q✉❛♥ ✈➲ ❜→♥ ❞➝♥ t❤➜♣ ❝❤✐➲✉ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷ ✶✳✷✳ ❚ê♥❣ q✉❛♥ ✈➲ ❣✐➳♥❣ ❧÷đ♥❣ tû ✈➔ s✐➯✉ ♠↕♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✶✳✷✳✶✳ ❚ê♥❣ q✉❛♥ ✈➲ ❣✐➳♥❣ ❧÷đ♥❣ tû ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ✶✳✷✳✷✳ ❚ê♥❣ q✉❛♥ ✈➲ s✐➯✉ ♠↕♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ▼Ð ✣❺❯ ◆❐■ ❉❯◆● ✶✳✸✳ ◆➠♥❣ ❧÷đ♥❣✱ ❤➔♠ sâ♥❣ ❝õ❛ ❡❧❡❝tr♦♥ tr♦♥❣ ❣✐➳♥❣ ❧÷đ♥❣ tû t❤➳ ✈✉ỉ♥❣ ❣â❝ s➙✉ ✈ỉ ❤↕♥ tr♦♥❣ tr÷í♥❣ ❤đ♣ ❝❤÷❛ ❝â ✈➔ ❝â tø tr÷í♥❣ t➽♥❤ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✶✳✸✳✶✳ ❚r÷í♥❣ ❤đ♣ ❝❤÷❛ ❝â tø tr÷í♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✶✳✸✳✷✳ ❚r÷í♥❣ ❤đ♣ ❝â tø tr÷í♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✶✳✹✳ ❍❛♠✐❧t♦♥✐❛♥ ❝õ❛ ❤➺ tr ữợ t trữớ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽ ✶✳✹✳✶✳ ❚r÷í♥❣ ❤đ♣ ♣❤♦♥♦♥ ❦❤è✐ ✭❦❤ỉ♥❣ ❜à ❣✐❛♠ ❣✐ú✮ ✳ ✳ ✳ ✳ ✶✽ ✶✳✹✳✷✳ ❚r÷í♥❣ ❤ñ♣ ♣❤♦♥♦♥ ❣✐❛♠ ❣✐ú ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✶✳✹✳✸✳ ❈→❝ ♠ỉ ❤➻♥❤ ♣❤♦♥♦♥ ❣✐❛♠ ❣✐ú tr♦♥❣ ❣✐➳♥❣ ❧÷đ♥❣ tû ✷✶ ✶ ✶✳✹✳✹✳ ❚➼♥❤ t❤ø❛ sè ❞↕♥❣ ❝õ❛ ❡❧❡❝tr♦♥ tr♦♥❣ ❣✐➳♥❣ ❧÷đ♥❣ tû ✤➦t tr♦♥❣ tø tr÷í♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✶✳✺✳ P❤÷ì♥❣ ♣❤→♣ t♦→♥ tû ❝❤✐➳✉ ❝æ ❧➟♣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✶✳✺✳✶✳ P❤÷ì♥❣ ♣❤→♣ t♦→♥ tû ❝❤✐➳✉ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✶✳✺✳✷✳ P❤÷ì♥❣ ♣❤→♣ t♦→♥ tû ❝❤✐➳✉ ❝ỉ ❧➟♣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✶✳✻✳ P❤÷ì♥❣ ♣❤→♣ Pr♦❢✐❧❡ ✤➸ ①→❝ ✤à♥❤ ✤ë rë♥❣ ♣❤ê ❤➜♣ t❤ö ✳ ✳ ✷✽ ❈❤÷ì♥❣ ✷✳ ❇■➎❯ ❚❍Ù❈ ●■❷■ ❚➑❈❍ ❈Õ❆ ❈➷◆● ❙❯❻❚ ❍❻P ❚❍Ö ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✷✳✶✳ ❚➻♠ ❜✐➸✉ t❤ù❝ t❡♥①ì ✤ë ❞➝♥ ✈➔ ❤➔♠ s✉② ❣✐↔♠ ❜➡♥❣ ♣❤÷ì♥❣ ♣❤→♣ ❝❤✐➳✉ ❝æ ❧➟♣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✷✳✶✳✶✳ ❇✐➸✉ t❤ù❝ tê♥❣ q✉→t ❝õ❛ t❡♥①ì ✤ë ❞➝♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✷✳✶✳✷✳ ❇✐➸✉ t❤ù❝ tê♥❣ q✉→t ❝õ❛ ❤➔♠ s✉② ❣✐↔♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✷✳✷✳ ❈ỉ♥❣ s✉➜t ❤➜♣ t❤ư tr♦♥❣ ❣✐➳♥❣ t❤➳ ✈✉ỉ♥❣ ❣â❝ s➙✉ ✈ỉ ❤↕♥ ✳ ✺✵ ✷✳✷✳✶✳ ❚r÷í♥❣ ❤đ♣ ♣❤♦♥♦♥ ❦❤è✐ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✷✳✷✳✷✳ ❚r÷í♥❣ ❤ñ♣ ♣❤♦♥♦♥ ❣✐❛♠ ❣✐ú ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✳ ✻✼ ✸✳✶✳ ✣✐➲✉ ❦✐➺♥ ❝ë♥❣ ❤÷ð♥❣ tø✲♣❤♦♥♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ❈❤÷ì♥❣ ✸✳ ❑➌❚ ◗❯❷ ❚➑◆❍ ❙➮ ❱⑨ ❚❍❷❖ ▲❯❾◆ ✸✳✷✳ ❈ë♥❣ ❤÷ð♥❣ tø ✲ ♣❤♦♥♦♥ ❣✐❛♠ ❣✐ú tr♦♥❣ ❣✐➳♥❣ ❧÷đ♥❣ tû t❤➳ ✈✉ỉ♥❣ ❣â❝ s➙✉ ✈ỉ ❤↕♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✸✳✸✳ ❙ü ♣❤ö t❤✉ë❝ ❝õ❛ ✤ë rë♥❣ ✈↕❝❤ ♣❤ê ❝õ❛ ✤➾♥❤ ❝ë♥❣ ❤÷ð♥❣ tø ✲ ♣❤♦♥♦♥ ✈➔♦ ♥❤✐➺t ✤ë ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✵ ✸✳✹✳ ❙ü ♣❤ư t❤✉ë❝ ❝õ❛ ✤ë rë♥❣ ✈↕❝❤ ♣❤ê ✈➔♦ tø tr÷í♥❣ ✳ ✳ ✳ ✳ ✳ ✼✷ ✸✳✺✳ ❙ü ♣❤ö t❤✉ë❝ ❝õ❛ ✤ë rë♥❣ ✈↕❝❤ ♣❤ê ❝õ❛ ✤➾♥❤ ❝ë♥❣ ❤÷đ♥❣ tø ✲ ♣❤♦♥♦♥ ✈➔♦ ❜➲ rë♥❣ ❣✐➳♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✹ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✼ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽ ❑➌❚ ▲❯❾◆ ❚⑨■ ▲■➏❯ ❚❍❆▼ ❑❍❷❖ ✷ P❍Ö ▲Ö❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ P✳✶ ✸ ❉❆◆❍ ▼Ư❈ ❈⑩❈ ❍➐◆❍ ❱⑨ ✣➬ ❚❍➚ ❍➻♥❤ ✶✳✶ ▼ỉ ❤➻♥❤ ❜→♥ ❞➝♥ ❦❤è✐✱ ❜→♥ ❞➝♥ t❤➜♣ ❝❤✐➲✉ ✈➔ ♠➟t ✤ë tr↕♥❣ t❤→✐ t÷ì♥❣ ù♥❣✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸ ❍➻♥❤ ✶✳✷ ❈➜✉ tró❝ ❝õ❛ ❣✐➳♥❣ ❧÷đ♥❣ tû ✤ì♥✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹ ❍➻♥❤ ✶✳✸ ▼✐♥❤ ❤å❛ ❝➜✉ t↕♦ ❝õ❛ s✐➯✉ ♠↕♥❣ t❤➔♥❤ ♣❤➛♥ ✭❛✮ ✈➔ s✐➯✉ ♠↕♥❣ ♣❤❛ t↕♣ ✭❜✮✳ ❍➻♥❤ ✶✳✹ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ❱❡❝tì A(t) ✤÷đ❝ ♣❤➙♥ t➼❝❤ t❤➔♥❤ ❤❛✐ t❤➔♥❤ ♣❤➛♥ ✈✉ỉ♥❣ ❣â❝ ✈ỵ✐ ♥❤❛✉ ❧➔ φ(t).A ✈➔ A (t) ❞ü❛ tr➯♥ ❦ÿ t❤✉➟t ❝❤✐➳✉ t♦→♥ tû ❝õ❛ ▼♦r✐✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ❍➻♥❤ ✶✳✺ ✷✻ ✣ë rë♥❣ ữủ t tứ ỗ t ổ st ❤➜♣ t❤ư ♣❤ư t❤✉ë❝ ✈➔♦ ♥➠♥❣ ❧÷đ♥❣ ♣❤♦t♦♥✳ ✳ ✳ ỗ t ỹ tở ❝ỉ♥❣ s✉➜t ❤➜♣ t❤ư ✈➔♦ ♥➠♥❣ ❧÷đ♥❣ ♣❤♦t♦♥ ω tr♦♥❣ ❣✐➳♥❣ ❧÷đ♥❣ tû t❤➳ ❤➻♥❤ ❝❤ú ♥❤➟t ✤➦t tr♦♥❣ tø tr÷í♥❣ tr♦♥❣ tr÷í♥❣ ❤đ♣ ♣❤♦♥♦♥ ❣✐❛♠ ❣✐ú ✭✤÷í♥❣ ♠➔✉ ①❛♥❤ ❧✐➲♥ ♥➨t✮ ✈➔ ♣❤♦♥♦♥ ❦❤è✐ ✭✤÷í♥❣ ♠➔✉ ✤ä ✤ùt ♥➨t✮ t↕✐ T = 300 ❑✱ Lz = 12 ♥♠✱ B = 12 ❚✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ỗ t ❙ü ♣❤ư t❤✉ë❝ ❝õ❛ ❝ỉ♥❣ s✉➜t ❤➜♣ t❤ư ✈➔♦ ♥➠♥❣ ❧÷đ♥❣ ♣❤♦t♦♥ t↕✐ ✤➾♥❤ ❝ë♥❣ ❤÷ð♥❣ tø ✲ ♣❤♦♥♦♥ ✭hΩ = 56.99 ♠❡❱✮ ✤è✐ ✈ỵ✐ ♠ỉ ❤➻♥❤ ❣✐❛♠ ❣✐ú t↕✐ ❝→❝ ❣✐→ trà ❦❤→❝ ♥❤❛✉ ❝õ❛ ♥❤✐➺t ✤ë✭❚❂✶✵✵ ❑✿ ✤÷í♥❣ ♥➨t ❧✐➲♥ ♠➔✉ ✤❡♥✱ ❚❂✷✵✵ ❑✿ ✤÷í♥❣ ✤ùt ♥➨t ♠➔✉ ①❛♥❤✱ ❚❂✸✵✵ ❑✿ ✤÷í♥❣ ❝❤➜♠ ❝❤➜♠ ♠➔✉ ✤ä✮✱ tr♦♥❣ tr÷í♥❣ ❤ñ♣ ❇❂✶✷ ❚✱ Lz = 12 ♥♠✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ỗ t ỹ tở ✤ë rë♥❣ ✈↕❝❤ ♣❤ê ❝õ❛ ✤➾♥❤ ❝ë♥❣ ❤÷ð♥❣ tø ✲ ♣❤♦♥♦♥ ✈➔♦ ♥❤✐➺t ✤ë tr♦♥❣ tr÷í♥❣ ❤đ♣ ♣❤♦♥♦♥ ❣✐❛♠ ❣✐ú ✭✤÷í♥❣ ỉ ❤➻♥❤ trá♥ ♠➔✉ ①❛♥❤✮ ✈➔ ♣❤♦♥♦♥ ❦❤è✐ ✭✤÷í♥❣ æ ❤➻♥❤ ✈✉æ♥❣ ♠➔✉ ✤ä✮✳ ✳ ✳ ✳ ✳ ✼✵ ỗ t ỹ tở ổ st tử ữủ t ố ợ ổ ❣✐❛♠ ❣✐ú t↕✐ ❝→❝ ❣✐→ trà ❦❤→❝ ♥❤❛✉ ❝õ❛ tø tr÷í♥❣ ❇✿ ❇❂✶✵ ❚ ✭✤÷í♥❣ ❧✐➲♥ ♥➨t ♠➔✉ ✤❡♥✮✱ ❇❂✶✷ ❚ ✭✤÷í♥❣ ✤ùt ♥➨t ♠➔✉ ①❛♥❤✮ ✈➔ ❇❂✶✺ ❚ ✭✤÷í♥❣ ❝❤➜♠ ❝❤➜♠ ♠➔✉ ✤ä✮ ✈ỵ✐ Lz = 12 ♥♠✱ ❚❂✸✵✵ ❑✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ỗ t ỹ tở rë♥❣ ✈↕❝❤ ♣❤ê ♣❤ư t❤✉ë❝ ✈➔♦ tø tr÷í♥❣ ❝❤♦ tr÷í♥❣ ❤đ♣ ♣❤♦♥♦♥ ❦❤è✐ ✭✤÷í♥❣ ỉ ❤➻♥❤ ✈✉ỉ♥❣ ♠➔✉ ✤ä✮ ✈➔ ♣❤♦♥♦♥ ❣✐❛♠ ❣✐ú ✭✤÷í♥❣ ỉ ❤➻♥❤ trá♥ ♠➔✉ ①❛♥❤✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ỗ t ỹ ♣❤ư t❤✉ë❝ ❝õ❛ ❝ỉ♥❣ s✉➜t ❤➜♣ t❤ư ✈➔♦ ♥➠♥❣ ❧÷đ♥❣ ♣❤♦t♦♥ t↕✐ ✤➾♥❤ ❝ë♥❣ ❤÷ð♥❣ tø ✲ ♣❤♦♥♦♥ tr♦♥❣ tr÷í♥❣ ❤ñ♣ ♣❤♦♥♦♥ ❣✐❛♠ ❣✐ú t↕✐ ❝→❝ ❣✐→ trà ❦❤→❝ ♥❤❛✉ ❝õ❛ ❜➲ rë♥❣ ❣✐➳♥❣ Lz ✿ Lz = 20 ♥♠ ✭✤÷í♥❣ ❧✐➲♥ ♥➨t ♠➔✉ ✤❡♥✮✱ Lz = 15 ♥♠ ✭✤÷í♥❣ ✤ùt ♥➨t ♠➔✉ ①❛♥❤✮ ✈➔ Lz = 10 ♥♠ ✭✤÷í♥❣ ❝❤➜♠ ❝❤➜♠ ♠➔✉ ✤ä✮ ✈ỵ✐ ❇ ❂ ✶✵ ❚✱ ❚ ❂ ✸✵✵ ❑✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ỗ t ỹ tở rë♥❣ ✈↕❝❤ ♣❤ê ♣❤ö t❤✉ë❝ ✈➔♦ ❜➲ rë♥❣ ❣✐➳♥❣ ❝❤♦ tr÷í♥❣ ❤đ♣ ♣❤♦♥♦♥ ❦❤è✐ ✭✤÷í♥❣ ỉ ❤➻♥❤ ✈✉ỉ♥❣ ♠➔✉ ✤ä✮ ✈➔ ♣❤♦♥♦♥ ❣✐❛♠ ❣✐ú ✭✤÷í♥❣ ỉ ❤➻♥❤ trá♥ ♠➔✉ ①❛♥❤✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✼✺ ▼Ð ✣❺❯ ■✳ ỵ t ữợ t tr ❝õ❛ ①➣ ❤ë✐ ♥❣➔② ♥❛② t❤➻ ♥❤✉ ❝➛✉ ❝õ❛ ❝♦♥ ♥❣÷í✐ ✈➲ ❦❤♦❛ ❤å❝ ❝ỉ♥❣ ♥❣❤➺ ♥❣➔② ❝➔♥❣ t➠♥❣ ❝❛♦✳ ✣➸ ✤→♣ ù♥❣ ✤÷đ❝ ♥❤✉ ❝➛✉ ✤â ✤á✐ ❤ä✐ ❝→❝ ♥❤➔ ❦❤♦❛ ❤å❝ ♣❤↔✐ t➻♠ r❛ ❝→❝ ✈➟t ❧✐➺✉ ♠ỵ✐ ợ t t ữủt trở ỡ ởt ố q trå♥❣ ✤→♥❤ ❞➜✉ sü ♣❤→t tr✐➸♥ ♥➔② ❝❤➼♥❤ ❧➔ ✈✐➺❝ ữợ ố tữủ ự tứ ố s❛♥❣ ❜→♥ ❞➝♥ t❤➜♣ ❝❤✐➲✉ ✈➔♦ ❝✉è✐ ♥❤ú♥❣ ♥➠♠ ✽✵ ❝õ❛ t❤➳ ❦✛ ✷✵✳ ✣â ❧➔ ❜→♥ ❞➝♥ ❤❛✐ ❝❤✐➲✉ ✭❣✐➳♥❣ ❧÷đ♥❣ tû✱ s✐➯✉ ♠↕♥❣✮✱ ❜→♥ ❞➝♥ ♠ët ❝❤✐➲✉ ✭❞➙② ❧÷đ♥❣ tû✮✱ ❜→♥ ❞➝♥ ❦❤ỉ♥❣ ❝❤✐➲✉ ✭❝❤➜♠ ❧÷đ♥❣ tû✮✳ ❱✐➺❝ t↕♦ r❛ ❜→♥ ❞➝♥ ❝â ❝➜✉ tró❝ t❤➜♣ ❝❤✐➲✉ ✤➣ ❣✐ó♣ ❝♦♥ ♥❣÷í✐ s→♥❣ ❝❤➳ r❛ ❝→❝ t❤✐➳t ❜à✱ ❧✐♥❤ ❦✐➺♥ ✤✐➺♥ tû s✐➯✉ ♥❤ä ✈➔ t❤æ♥❣ ♠✐♥❤✳ ✣➣ ❝â ♥❤✐➲✉ ♣❤÷ì♥❣ ♣❤→♣ ✤÷đ❝ ✤➲ ①✉➜t ✤➸ ♥❣❤✐➯♥ ❝ù✉ ❝→❝ t➼♥❤ ❝❤➜t ❝õ❛ ❤➺ t❤➜♣ ❝❤✐➲✉ ♥❤÷✿ ♣❤÷ì♥❣ ♣❤→♣ ❣➛♥ ú t ữớ tt ỗ ♣❤÷ì♥❣ ♣❤→♣ t♦→♥ tû ❝❤✐➳✉✱✳✳✳✳ ▼é✐ ♣❤÷ì♥❣ ♣❤→♣ ♥❣❤✐➯♥ ❝ù✉ ✤➲✉ ❝â ♥❤ú♥❣ ÷✉ ✤✐➸♠ ✈➔ ♥❤÷đ❝ ✤✐➸♠ r✐➯♥❣ ❝õ❛ ♥â✳ ❚r♦♥❣ ❝→❝ ♣❤÷ì♥❣ ♣❤→♣ tr➯♥✱ t♦→♥ tû ❝❤✐➳✉ ❧➔ ữỡ ữủ sỷ t ỵ ✈ỵ✐ ❝→❝ t♦→♥ tû ❝❤✐➳✉ ❤♦➔♥ t♦➔♥ ①→❝ ✤à♥❤✱ t❛ ❝â t❤➸ t❤✉ ✤÷đ❝ ❝ỉ♥❣ t❤ù❝ ✤ë ❞➝♥ ❦❤→ ❤♦➔♥ ❤↔♦✱ ❜✐➸✉ t❤ù❝ ❤➔♠ ❞↕♥❣ ♣❤ê t÷í♥❣ ♠✐♥❤✳ ❈→❝ ♥❤➔ ❦❤♦❛ ❤å❝ ✤➣ ❝â r➜t ♥❤✐➲✉ ♥❣❤✐➯♥ ❝ù✉ ✈➲ ↔♥❤ ữ tữỡ t tr ố ợ t➼♥❤ ❝❤➜t q✉❛♥❣ ❤å❝ ❝õ❛ ❤➺ ❡❧❡❝tr♦♥ ❤❛✐ ❝❤✐➲✉✱ ✤÷đ❝ ❤➻♥❤ t❤➔♥❤ tr♦♥❣ ❝→❝ ❧ỵ♣ ❞à t✐➳♣ ①ó❝ ❜→♥ ❞➝♥ ✈➔ ❝→❝ ❣✐➳♥❣ ❧÷đ♥❣ tû ❦❤✐ ❝â ♠➦t ❝õ❛ tø tr÷í♥❣ ❧÷đ♥❣ tû ❬✷✵❪✳ Ð ❝➜✉ ✻ (Γ± N +1,N ) 1 d3 q [N + ± ] × |V (q)|2 |K(N, N ; t)|2 |Gn,n (qz )| q (2π) 2 = ❚❤❛② ❜✐➸✉ t❤ù❝ ❝õ❛ K(N, N ; t) ✈➔ |V (q)|2 ✈➔♦ ♣❤÷ì♥❣ tr➻♥❤ tr➯♥ t❛ ✤÷đ❝ (Γ± N,N ) e ωq ∗ 1 = χ (N + ± ) q 16π ε0 2 ∞ +∞ × |Gn,n (qz )|dqz −∞ q⊥ K(N, N ; t) dq⊥ (q⊥ + qd2 ) ❚❛ ❧➛♥ ❧÷đt t➼♥❤ ❝→❝ sè ❤↕♥❣ ❞❡❧t❛ ♥❤÷ s❛✉✿ sè ❤↕♥❣ ✭✶✮ δ( ω − (N − N ) ωc + (En − En ) − ωq ) Γ± N,N = , π [ ω − (N − N ) ωc + (En − En ) − ωq ]2 − (Γ± N,N ) ✭P✳✽✮ tr♦♥❣ ✤â (Γ± N,N ) = e2 ωq ∗ χ (Nq ) 16π ε0 ∞ +∞ × |Gn,n (qz )|dqz −∞ q⊥ dq⊥ K(N, N ; t) (q⊥ + qd2 ) ❚÷ì♥❣ tü ✈ỵ✐ sè ❤↕♥❣ ✭✷✮ δ( ω − (N − N ) ωc + (En − En ) + ωq ) Γ± N,N , = π [ ω − (N − N ) ωc + (En − En ) − ωq ]2 − (Γ± N,N ) tr♦♥❣ ✤â (Γ± N,N ) e2 ωq ∗ χ (Nq + 1) = 16π ε0 ∞ +∞ × |Gn,n (qz )|dqz −∞ q⊥ dq⊥ K(N, N ; t) (q + qd2 ) ữỡ tỹ ợ số ❤↕♥❣ ✭✸✮ δ( ω − (N − N − 1) ωc + (En − En ) − ωq ) P✳✹ ✭P✳✾✮ Γ± N,N , ✭P✳✶✵✮ = π [ ω − (N − N − 1) ωc + (En − En ) − ωq ]2 − (Γ± N,N ) tr♦♥❣ ✤â (Γ± N,N ) = e ωq ∗ χ (Nq ) 16π ε0 ∞ +∞ × |Gn,n (qz )|dqz −∞ q⊥ K(N, N ; t) dq⊥ (q⊥ + qd2 ) ❚÷ì♥❣ tü ✈ỵ✐ sè ❤↕♥❣ ✭✹✮ δ( ω − (N − N − 1) ωc + (En − En ) − ωq ) Γ± N,N = , ✭P✳✶✶✮ π [ ω − (N − N − 1) ωc + (En − En ) − ωq ]2 − (Γ± ) N,N tr♦♥❣ ✤â (Γ± N,N ) e ωq ∗ χ (Nq + 1) = 16π ε0 ∞ +∞ × |Gn,n (qz )|dqz −∞ dq⊥ q⊥ + q ) K(N, N ; t) (q⊥ d ✰ ❚r÷í♥❣ ❤đ♣ ♣❤♦♥♦♥ ❣✐❛♠ ❣✐ú δ(E1± ) Γ± Γ± 1 N,N N +1,N ± = ; δ(E2 ) = ± ± ± 2 π (E1 ) − (ΓN,N ) π (E1 ) − (Γ± N +1,N ) ✣➦t E1± = ω − (Eβ − Eα ) ± ωq⊥ ,m = ω − (N − N ) ωc + (En − En ) ± ωq⊥,m , E2± = ω − (Eβ − Eα+1 ) ± ωm,q⊥ = ω − (N − N − 1) ωc + (En − En ) ± ωq⊥ ,m tr♦♥❣ ✤â (Γ± N,N ) = d3 q 1 [N + ± ] × |V (q)|2 |K(N, N ; t)|2 |Gmα q ,m n,n (qz )| ⊥ (2π) 2 P✳✺ (Γ± N +1,N ) 1 d3 q [N + ± ] × |V (q)|2 |K(N, N ; t)|2 |Gmα q ,m n,n (qz )| ⊥ (2π) 2 = ❚❤❛② ❜✐➸✉ t❤ù❝ ❝õ❛ K(N, N ; t) ✈➔ |V (q)|2 ✈➔♦ ♣❤÷ì♥❣ tr➻♥❤ tr➯♥ t❛ ✤÷đ❝ (Γ± N,N ) e2 ωq⊥,m ∗ 1 = χ (N + ± ) q ,m ⊥ 16π ε0 2 ∞ +∞ × |Gn,n (qz )|dqz −∞ q⊥ K(N, N ; t) dq⊥ (q⊥ + qd2 ) ❚❛ ❧➛♥ ❧÷đt t➼♥❤ ❝→❝ sè ❤↕♥❣ ❞❡❧t❛ ♥❤÷ s❛✉✿ sè ❤↕♥❣ ✭✶✮ δ( ω − (N − N ) ωc + (En − En ) − ωq⊥ ,m ) Γ± N,N = , π [ ω − (N − N ) ωc + (En − En ) − ωq⊥ ,m ]2 − (Γ± N,N ) ✭P✳✶✷✮ tr♦♥❣ ✤â (Γ± N,N ) = e2 ωq⊥,m ∗ χ (Nq⊥,m ) 16π ε0 ∞ +∞ × −∞ |Gmα n,n (qz )|dqz q⊥ dq⊥ K(N, N ; t) (q⊥ + qd2 ) ữỡ tỹ ợ số ( − (N − N ) ωc + (En − En ) + ωq⊥,m ) Γ± N,N , ✭P✳✶✸✮ = π [ ω − (N − N ) ωc + (En − En ) − ωq⊥,m ]2 − (Γ± N,N ) tr♦♥❣ ✤â (Γ± N,N ) e ωq ∗ χ (Nq⊥,m + 1) = 16π ε0 ∞ +∞ × −∞ |Gmα n,n (qz )|dqz q⊥ dq⊥ K(N, N ; t) (q⊥ + qd2 ) ữỡ tỹ ợ số ( − (N − N − 1) ωc + (En − En ) − ωq⊥,m ) P✳✻ Γ± N,N , = π [ ω − (N − N − 1) ωc + (En − En ) − ωq⊥,m ]2 − (Γ± N,N ) ✭P✳✶✹✮ tr♦♥❣ ✤â (Γ± N,N ) e2 ωq⊥,m ∗ = χ (Nq⊥,m ) 16π ε0 ∞ +∞ × −∞ |Gmα n,n (qz )|dqz q⊥ dq⊥ K(N, N ; t) (q⊥ + qd2 ) ữỡ tỹ ợ số ( ω − (N − N − 1) ωc + (En − En ) − ωq⊥,m ) Γ± N,N = , π [ ω − (N − N − 1) ωc + (En − En ) − ωq⊥,m ]2 − (Γ± N,N ) ✭P✳✶✺✮ tr♦♥❣ ✤â (Γ± N,N ) e2 ωq⊥,m ∗ χ (Nq⊥,m + 1) = 16π ε0 ∞ +∞ × −∞ |Gmα n,n (qz )|dqz q⊥ K(N, N ; t) dq⊥ (q⊥ + qd2 ) P❤ö ❧ö❝ ✺ ✰ ❚➼♥❤ t❤ø❛ sè ❞↕♥❣ tr♦♥❣ tr÷í♥❣ ❤đ♣ ♣❤♦♥♦♥ ❦❤è✐ Gnn (qz ) = n|eiqz z |n = = Lz Lz /2 sin( −Lz /2 = Lz n πz nπ iqz z nπz n π + + )e sin( )dz Lz Lz Lz /2 cos[ −Lz /2 ϕn (z)eiqz z ϕn (z)dz (n − n )πz (n − n )π (n + n )πz (n + n )π iqz z + ] − cos[ + ] e d Lz Lz P✳✼ = Lz Lz /2 cos[ −Lz /2 Lz (n − n)πz (n − n )π iqz z + ]e dz Lz (n + n )πz (n + n )π iqz z ]e dz cos[ + Lz Lz = (C − D) Lz − ❑❤✐ n = n ✱ ✤➦t   u = eiqz z  dv = cos[ (n−n )πz + Lz ⇒ (n−n )π ]dz   du = iq eiqz z z  v = Lz sin[ (n−n )πz + (n−n )π Lz (n−n )π ] Lz (n − n )πz (n − n )π Lz /2 + eiqz z sin[ ]|−Lz /2 (n − n )π Lz Lz /2 (n − n )πz (n − n )π iqz Lz eiqz z sin[ + ]dz − (n − n )π −Lz /2 Lz C= iqz Lz = (n − n )π ✣➦t ⇒ Lz /2 eiqz z sin[ −Lz /2 (n − n )πz (n − n )π + ]dz Lz   u = eiqz z  dv = sin[ (n−n )πz + Lz (n−n )π ]dz   du = iq eiqz z z  v = − Lz cos[ (n −n)πz + (n−n )π Lz (n−n )π ] iqz Lz (n − n )πz (n − n )π eiqz z Lz C= cos[ + ] − (n − n )π (n − n )π Lz iqz Lz − (n − n )π Lz /2 −Lz /2 eiqz z cos[ (n − n )πz (n − n )π + ] dz Lz P✳✽ ✭P✳✶✻✮ Lz /2 −Lz /2 qz2 L2z iqz L2z iqz z [e cos(n − n)π − 1] + A, = (n − n )2 π (n − n )2 π ⇒C= iqz L2z iqz z (n−n )2 π [e 1− cos(n − n)π − 1] qz2 L2z (n−n )2 π iqz z cos(n − n )πz − (n − n )2 π − qz2 L2z iqz z (−1)n−n − e = iqz Lz (n − n )2 π − qz2 L2z iqz z (−1)n+n − e = iqz Lz (n − n )2 π − qz2 L2z = e iqz L2z ❚÷ì♥❣ tü t❛ ❝ơ♥❣ t➼♥❤ ✤÷đ❝✿ D= eiqz z (−1)n+n − (n + n )2 π − qz2 L2z iqz L2z ❱➟② Gn,n = (C − D) Lz = iqz Lz [eiqz z (−1)n +n − 1] × (n − n )2 π − qz2 L2z − (n + n )2 π − qz2 L2z = iqz Lz [eiqz z (−1)n +n − 1] × 4nn π π (n − n2 )2 − 2qz2 L2z π (n − n2 ) + qz4 L4z ✭P✳✶✼✮ ❚❤❛② ♥❂✶ ✈➔ ♥✬❂✷ ✈➔♦ t❛ ✤÷đ❝ G1,2 8i(1 + eiLz qz )Lz π qz =− 9π − 10L2z π qz2 + L4z qz4 64(1 + e−iLz qz )(1 + eiLz qz )L2z π qz2 |G1,2 | = − (9π − 10L2z π qz2 + L4z qz4 )2 ✰ ❚➼♥❤ t❤ø❛ sè ❞↕♥❣ tr♦♥❣ tr÷í♥❣ ❤đ♣ ♣❤♦♥♦♥ ❣✐❛♠ ❣✐ú P✳✾ ✭P✳✶✽✮ P ố ợ ữủ tỷ t ổ õ s ✈æ ❤↕♥✱ t❤ø❛ sè ❞↕♥❣ Gmα nn ❝â ❞↕♥❣ Gmα nn (qz ) Lz /2 = −Lz /2 ψn∗ (z)umα (z)ψn (z)dz ✭P✳✷✵✮ ❳➨t ❞à❝❤ ❝❤✉②➸♥ ❣✐ú❛ ❤❛✐ ♠ù❝ ♥ë✐ ✈ò♥❣ ❝♦♥ t❤➜♣ ♥❤➜t (n = n = 1)✱ t❛ ✤÷đ❝ Gm+ 11 = Lz = = = Lz Lz Lz −Lz /2 Lz /2 sin2 ( µm πz πz π cm + )[sin( ) + z]dz Lz Lz Lz cos2 ( −Lz /2 Lz /2 πz µm πz cm )[sin( ) + z]dz Lz Lz Lz [1 + cos( −Lz /2 Lz /2 [sin( −Lz /2 Lz /2 µm πz cm 2πz )][sin( ) + z]dz Lz Lz Lz µm πz cm 2πz µm πz 2πz cm ) + z + cos( ) sin( ) + cos( ) z]dz Lz Lz Lz Lz Lz Lz µm πz cm (µm + 2)π ) + z + [sin( z) L L L z z z −Lz /2 (µm − 2)π 2πz cm + sin( z)] + cos( ) z}dz Lz Lz Lz Lz cm µm πz Lz (µm + 2)π = {− )+ z) cos( z + [− cos( Lz µm π Lz Lz 2 (µm + 2)π Lz Lz /2 Lz (µm − 2)π 2πz cm Lz /2 − cos( z)]}|−Lz /2 + cos( ) zdz (µm − 2)π Lz Lz −Lz /2 Lz Lz Lz µm π µm π cm L2z L2z [cos( ) − cos( )] + [ − ] = {− Lz µm π 2 Lz 4 Lz (µm + 2)π (µm + 2)π + [− [cos( ) − cos( )] (µm + 2)π 2 Lz /2 Lz (µm − 2)π (µm − 2)π 2πz cm − [cos( ) − cos( )]]} + cos( ) zd (µm + 2)π 2 Lz −Lz /2 Lz Lz = Lz Lz /2 = Lz = {sin( Lz /2 2πz cm cm cos( ) zdz = Lz Lz Lz −Lz /2 cm Lz L2z 2π Lz /2 zd(sin( −Lz /2 2πz ))dz Lz P✳✶✵ Lz /2 z cos( −Lz /2 2πz )dz Lz Lz /2 cm Lz 2πz Lz /2 2πz = [z sin( )|−Lz /2 − sin( )dz] Lz 2π Lz Lz −Lz /2 2πz Lz /2 Lz 2πz Lz /2 cm Lz )|−Lz /2 + cos( )| ] = [z sin( Lz 2π Lz 2π Lz −Lz /2 cm Lz Lz Lz = [ sin π − sin π + (cos π − cos π)] = 0, m = 3, 5, 7, 2πLz 2 2π ✭P✳✷✶✮ ❳➨t ❞à❝❤ ❝❤✉②➸♥ ❣✐ú❛ ❤❛✐ ♠ù❝ ♥ë✐ ✈ò♥❣ ❝♦♥ t❤➜♣ ♥❤➜t (n = n = 1)✱ t❛ ✤÷đ❝ Gm− 11 = Lz = = = Lz Lz Lz Lz /2 −Lz /2 Lz /2 sin2 ( mπz πz π + )[cos( ) − (−1)m/2 ]dz Lz Lz cos2 ( −Lz /2 Lz /2 πz mπz )[cos( ) − (−1)m/2 ]dz Lz Lz [1 + cos( −Lz /2 Lz /2 [cos( −Lz /2 2πz mπz )][cos( ) − (−1)m/2 ]dz Lz Lz mπz 2πz mπz ) − (−1)m/2 + cos( ) cos( ) Lz Lz Lz 2πz )(−1)m/2 ]dz Lz Lz /2 mπz (2 + m)πz = [cos( ) − (−1)m/2 + [cos( ) Lz −Lz /2 Lz Lz (2 − m)πz 2πz + cos( )] − cos( )(−1)m/2 ]dz Lz Lz mπz Lz (2 + mπz) Lz { sin( ) − (−1)m/2 z + [ sin( ) Lz mπ Lz (2 + m)πz Lz Lz (2 − m)πz Lz 2πz Lz /2 + sin( )] − sin( )(−1)m/2 }|−L z /2 (2 − m)π Lz 2π Lz mπ Lz −Lz Lz sin( ) − (−1)m/2 ( − ) = { Lz mπ 2 Lz (2 + m)π + [ sin( ) (2 + m)π Lz (2 − m)π Lz + sin( )] − sin(π)(−1)m/2 } (2 − m)π 2π − cos( P✳✶✶ Lz mπ Lz (2 + m)π sin( ) − (−1)m/2 Lz + [ sin( ) { Lz mπ 2 (2 + m)π Lz (2 − m)π + sin( )]}, m = 2, 4, 6, ✭P✳✷✷✮ (2 − m)π = ❑❤✐ m = 2✱ t❛ ❝â mπ Lz (2 + m)π Lz { sin( ) − (−1)m/2 Lz + [ sin( ) Lz mπ 2 (2 + m)π Lz (2 − m)π sin( )]} = −(−1)m/2 ✭P✳✷✸✮ + (2 − m)π Gm− 11 = ❑❤✐ m = 2✱ t❛ ❝â Gm− 11 = Lz = = = Lz Lz Lz Lz /2 −Lz /2 Lz /2 sin2 ( mπz πz π + )[cos( ) − (−1)m/2 ]dz Lz Lz cos2 ( −Lz /2 Lz /2 πz 2πz )[cos( ) + 1]dz Lz Lz [1 + cos( −Lz /2 Lz /2 [cos( −Lz /2 Lz /2 2πz 2πz )][cos( ) + 1]dz Lz Lz 2πz 2πz 2πz ) + + cos2 ( ) + cos( )]dz Lz Lz Lz 2πz 4πz 2πz [cos( ) + + [1 + cos( )] + cos( )]dz Lz −Lz /2 Lz Lz Lz Lz 2πz Lz 4πz Lz 2πz Lz /2 = { sin( ) + z + [z + sin( )] + sin( )}|−Lz /2 Lz 2π Lz 4π Lz 2π Lz Lz Lz L z Lz L z Lz Lz = { sin(π) + ( − ) + [( − ) + sin(2π)] + sin(π)} Lz 2π 2 2 4π 2π = ✭P✳✷✹✮ = ❦➳t ❤ñ♣ ✭P✳✷✸✮ ✈➔ ✭P✳✷✹✮✱ t❛ t❤✉ ✤÷đ❝ Gm− = δm,2 − (−1)m/2 (1 − δm,2 ), m = 2, 4, 11 ✭P✳✷✺✮ ❳➨t ❞à❝❤ ❝❤✉②➸♥ ❣✐ú❛ ❤❛✐ ♠ù❝ ❧✐➯♥ ✈ò♥❣ ❝♦♥ t❤➜♣ ♥❤➜t (n = 1, n = 2)✱ t❛ ✤÷đ❝ Gm+ 12 = Lz Lz /2 sin( −Lz /2 πz π µm πz cm 2πz + )[sin( ) + z] sin( + π)dz Lz Lz Lz Lz P✳✶✷ = Lz =− =− Lz Lz Lz /2 cos( −Lz /2 Lz /2 µm πz cm 2πz πz )[sin( ) + z][− sin( )]dz Lz Lz Lz Lz cos( −Lz /2 Lz /2 µm πz cm 2πz πz )[sin( ) + z] sin( )dz Lz Lz Lz Lz {cos( −Lz /2 Lz /2 πz µm πz 2πz πz cm 2πz ) sin( ) sin( ) + cos( ) z sin( )}dz Lz Lz Lz Lz Lz Lz (µm + 2)πz πz (µm − 2)πz ){− [cos( ) − cos( )]} L L L z z z −Lz /2 3πz πz cm ) + sin( )]}}dz + z{ [sin( Lz Lz Lz Lz /2 πz (µm + 2)πz πz (µm − 2)πz = cos( ) cos( ) − cos( ) cos( ) Lz −Lz /2 Lz Lz Lz Lz 3πz cm πz cm − z sin( ) − z sin( ) dz Lz Lz Lz Lz Lz /2 1 (µm + 3)πz (µm + 1)πz = [cos( ) + cos( )] Lz −Lz /2 Lz Lz (µm − 1)πz (µm − 3)πz cm 3πz cm πz − [cos( ) + cos( )] − z sin( ) − z sin( ) dz Lz Lz Lz Lz Lz Lz Lz (µm + 3)πz Lz (µm + 1)πz sin( )+ sin( ) = Lz 2(µm + 3)π Lz 2(µm + 1)π Lz =− Lz {cos( Lz (µm − 1)πz Lz (µm − 3)πz − sin( )− sin( ) 2(µm − 1)π Lz 2(µm − 3)π Lz Lz /2 −Lz /2 − I1 − I2 (µm + 3)π (µm + 1)π sin( )+ sin( ) (µm + 3)π (µm + 1)π (µm − 1)π (µm − 3)πz − sin( )− sin( ) − I1 − I2 (µm − 1)π (µm − 3)π 3π µm π π µm π = sin( + )+ sin( + ) (µm + 3)π 2 (µm + 1)π 2 −π µm π −3π µm π − sin( + )− sin( + ) − I1 − I2 (µm − 1)π 2 (µm − 3)π 2 µm π µm π =− cos( )+ cos( ) (µm + 3)π (µm + 1)π = P✳✶✸ µm π µm π cos( )− cos( ) − I1 − I2 (µm − 1)π (µm − 3)π 2µm µm π 1 = cos( ) − − I1(1.49) − I2(1.49), π µm − µ − + ✭P✳✷✻✮ tr♦♥❣ ✤â I1(1.41) = Lz =− Lz /2 cm 3πz cm Lz z sin( )dz = − Lz Lz Lz 3π −Lz /2 Lz cm 3πLz Lz /2 zd(cos( −Lz /2 cm 3πz ) z cos( =− 3πLz Lz Lz /2 zd(cos( −Lz /2 3πz ))dz Lz Lz /2 Lz /2 − cos( −Lz /2 −Lz /2 cm cm 3πz =− − z cos( ) 3πLz 3πLz Lz 3πz )dz Lz Lz /2 Lz 3πz − sin( ) 3π Lz −Lz /2 cm Lz 3π Lz 3π 2cm cos( ) − sin( ) = − , 3πLz 2 3π 9π Lz /2 cm πz z sin( )dz I2(1.41) = Lz −Lz /2 Lz Lz =− cm Lz =− Lz Lz π =− cm πLz Lz /2 zd(cos( −Lz /2 Lz /2 zd(cos( −Lz /2 −Lz /2 ✭P✳✷✼✮ πz ))dz Lz Lz /2 cm πz =− z cos( ) πLz Lz Lz πz − sin( ) π Lz −Lz /2 Lz /2 − cos( −Lz /2 −Lz /2 Lz /2 πz )dz Lz Lz /2 −Lz /2 cm Lz π Lz π 2cm cos( ) − sin( ) = πLz 2 2 π t❤❛② ✭P✳✷✼✮ ✈➔ ✭P✳✷✽✮ ✈➔♦ ✭P✳✷✻✮✱ t❛ t❤✉ ✤÷đ❝ Gm+ 12 = − Lz /2 πz ))dz Lz πz cm =− z cos( ) πLz Lz =− 3πz ))dz Lz 16cm 2µm µm π 1 + cos( ) − 9π π µ2m − µm − P✳✶✹ ✭P✳✷✽✮ 16cm 9π 16cm =− 9π 2cm =− π =− 2µm cm 1 [− ] − π µm π µm − µm − 2cm 1 − − π µ2m − µm − + − , m = 3, 5, 7, µm − µm − + ✭P✳✷✾✮ ❳➨t ❞à❝❤ ❝❤✉②➸♥ ❣✐ú❛ ❤❛✐ ♠ù❝ ❧✐➯♥ ✈ò♥❣ ❝♦♥ t❤➜♣ ♥❤➜t (n = 1, n = 2)✱ t❛ ✤÷đ❝ Gm− 12 Lz /2 = Lz = sin( −Lz /2 Lz /2 Lz =− mπ πz π 2πz + ) cos( z) − (−1)m/2 sin( + π)dz Lz Lz Lz cos( Lz −Lz /2 Lz /2 mπ 2πz πz ) cos( z) − (−1)m/2 [− sin( )]dz Lz Lz Lz cos( −Lz /2 Lz /2 πz mπ 2πz ) cos( z) − (−1)m/2 [sin( )]dz Lz Lz Lz πz mπ 2πz [cos( ) cos( z) sin( ) Lz −Lz /2 Lz Lz Lz πz 2πz − cos( )(−1)m/2 sin( )]dz = I1(1.53) − I2(1.53), Lz Lz =− ✭P✳✸✵✮ tr♦♥❣ ✤â I1(1.53) = − Lz =− =− =− Lz Lz Lz Lz /2 cos( πz mπ 2πz ) cos( z) sin( )dz Lz Lz Lz cos( πz (2 + m)πz (2 − m)πz ) sin( ) + sin( ) dz Lz Lz Lz −Lz /2 Lz /2 −Lz /2 Lz /2 cos( −Lz /2 Lz /2 −Lz /2 πz (2 + m)πz πz (2 − m)πz ) sin( ) + cos( ) sin( ) dz Lz Lz Lz Lz (3 + m)πz (1 − m)πz [sin( ) + sin( )] dz = Lz Lz P ữợ t I1(1.53) ❧➔ ❤➔♠ ❧➫ ♥➯♥ ❦➳t q✉↔ t➼❝❤ ♣❤➙♥ ❝❤♦ ❜➡♥❣ ❦❤ỉ♥❣ ✈➔ ❦❤ỉ♥❣ ♣❤ư t❤✉ë❝ ✈➔♦ ❣✐→ trà ♠✳ I2(1.53) = − Lz Lz /2 cos( −Lz /2 πz 2πz )(−1)m/2 sin( )dz Lz Lz P✳✶✺ = − (−1)m/2 Lz =− (−1)m/2 Lz Lz /2 cos( 2πz πz ) sin( )dz Lz Lz [sin( πz 3πz ) + sin( )]dz = 0, Lz Lz −Lz /2 Lz /2 −Lz /2 ✭P✳✸✷✮ t❤❛② ✭P✳✸✶✮ ✈➔ ✭P✳✸✷✮ ✈➔♦ ✭P✳✸✵✮✱ t❛ t❤✉ ✤÷đ❝ Gm− 12 = 0, m = 2, 4, 6, ✭P✳✸✸✮ P❤ö ❧ö❝ ✻ ✰ ❚➼♥❤ t➼❝❤ ♣❤➙♥ ❆ A= Lz ∞ Lz /2 dqz −∞ Lz /2 × dz sin( −Lz /2 dz sin( −Lz /2 ∞ = L2z nπ nπ n πz nπz + + )exp(iqz z ) sin( ) Lz Lz Lz /2 dqz exp[iqz (z − z )] −∞ Lz /2 × −Lz /2 Lz /2 dz sin( = = 8π L2z 8π L2z 2π = Lz −Lz /2 Lz /2 nπz nπ n πz n π + ) sin( + ) Lz Lz nπz nπ n πz nπ + ) sin( + ) Lz Lz = 2πδ(z − z ) Lz −Lz /2 Lz /2 dz sin( −Lz /2 dz sin( × n πz n π nπz nπ + + )exp(iqz z) sin( ) Lz Lz Lz /2 dz sin( −Lz /2 nπz nπ n πz n π + ) sin( + ) Lz Lz nπz nπ n πz nπ + ) sin( + ) Lz Lz dz sin2 ( nπz nπ n πz n π + ) sin2 ( + ) Lz Lz 2nπz 2n πz dz [1 − cos( + nπ)] [1 − cos( + n π)] Lz Lz −Lz /2 Lz /2 dz[1 − cos( −Lz /2 2nπz 2n πz + nπ)][1 − cos( + n π)] Lz Lz P✳✶✻ Lz /2 2π = Lz 2n πz 2nπz + nπ) − cos( + n π) Lz Lz −Lz /2 2n πz 2nπz + nπ) cos( + n π)] + cos( Lz Lz Lz /2 Lz /2 Lz Lz 2π 2n πz 2nπz − − = z sin( + n π) sin( + nπ) Lz 2n π Lz 2nπ Lz −Lz /2 −Lz /2 dz[1 − cos( Lz /2 −Lz /2 Lz /2 2n πz 2nπz + n π) cos( + nπ) Lz Lz −Lz /2 2π Lz Lz Lz Lz = [Lz − sin(2n π) + sin(0) − sin(2nπ) + sin(0) Lz 2n πz 2n πz 2n πz 2n πz + dz cos( + I1 ] 2π 2π = [Lz − + − + + I1 ] = [Lz + I1 ], Lz Lz ✭P✳✸✹✮ tr♦♥❣ ✤â Lz /2 I1 = dz cos( −Lz /2 2nπz 2n πz + n π) cos( + nπ) Lz Lz ✭P✳✸✺✮ ❑❤✐ n = n ✱ t❛ ❝â Lz /2 I1 = dz cos( −Lz /2 Lz /2 = 2n πz 2nπz + n π) cos( + nπ) Lz Lz dz cos[ −Lz /2 + cos[ 2(n − n )πz + (n − n )π] Lz 2(n − n )πz + (n − n )π] Lz Lz 2(n − n )πz = sin[ + (n − n )π] 2(n − n )π Lz + = Lz 2(n + n )πz sin[ + (n + n )π] 2(n + n )π Lz Lz /2 −Lz /2 Lz /2 −Lz /2 Lz Lz sin[2(n − n )π] − sin 2(n − n )π 2(n − n )π P✳✶✼ + Lz Lz sin[2(n + n )π] − sin 2(n + n )π 2(n + n )π ✭P✳✸✻✮ = ❑❤✐ n = n ✱ t❛ ❝â Lz /2 I1 = dz cos( −Lz /2 Lz /2 = 2n πz 2nπz + n π) cos( + nπ) Lz Lz dz cos2 ( −Lz /2 Lz /2 2nπz + nπ) Lz 4nπz dz[1 + cos( + 2nπ)] −Lz /2 Lz 4nπz Lz /2 Lz Lz /2 + ] sin( + 2nπ)|−L = [z|−L z /2 z /2 4nπ Lz Lz Lz = [Lz + sin(4nπ) − sin 0] 4nπ 4nπ Lz = = ✭P✳✸✼✮ ❚ø ✭P✳✸✻✮ ✈➔ ✭P✳✸✼✮ t❛ ✤÷đ❝ I1 = Lz δn,n , ✭P✳✸✽✮ ❚❤❛② ✈➔♦ ✭P✳✸✽✮ t❛ t❤✉ ✤÷đ❝ ∞ dqz |Gnn (qz )|2 = A= −∞ P✳✶✽ π (2 + δn,n ) Lz ✭P✳✸✾✮ ... ✭✶✳✸✷✮ ✣è✐ ✈ỵ✐ ♠♦❞❡ ❝❤➤♥ um− = cos(µπz/Lz ) − (−1)m/2 , m = 2, 4, 6, ✭✶✳✸✸✮ tr♦♥❣ ✤â µm ❧➔ tử ữỡ tr tan(àm /2) = àm /2, m < àm < m, ợ (à1 ) ❧➔ ♥❤ä ♥❤➜t ♥➯♥ ❜ä q✉❛ ✈➔ Cm ✤÷đ❝ ❝❤♦ ❜ð✐ Cm =... ❤➜♣ t❤ö ❜➡♥❣ ♠ët ♥û❛ ❣✐→ trà ❝ü❝ ✤↕✐ ❝õ❛ ♥â✳ ✷✽ ❍➻♥❤ ✶✳✺✿ ✣ë rë♥❣ ✈↕❝❤ ♣❤ê ✤÷đ❝ t tứ ỗ t ổ st tử t❤✉ë❝ ✈➔♦ ♥➠♥❣ ❧÷đ♥❣ ♣❤♦t♦♥✳ ✣ë rë♥❣ ✈↕❝❤ ♣❤ê ❧➔ tữợ s t ữớ ❤÷ð♥❣✱ ❝❤ó♥❣ ♣❤ư t❤✉ë❝ ✈➔♦ t➼♥❤