# 查看完整版本 : 量子力學上的哈密頓問題

xianrenb 2022-3-21 13:35

H = T + V

[url=https://en.wikipedia.org/wiki/Hamiltonian_mechanics]https://en.wikipedia.org/wiki/Hamiltonian_mechanics[/url]
Deriving_Hamilton's_equations 一節：
H = (Σ_i p_i q_i_dot ) - L

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sylim 2022-3-22 15:10

rhwlam 2022-3-23 18:01

q是state, 不一定是空間. q從來也是一個function of time.

Porky_Pig 2022-3-23 21:43

[quote]原帖由 [i]xianrenb[/i] 於 2022-3-21 13:35 發表 [url=https://www.discuss.com.hk/redirect.php?goto=findpost&pid=546791960&ptid=30484421][img]https://www.discuss.com.hk/images/common/back.gif[/img][/url]

H = T + V

https://en.wikipedia.org/wiki/Hamiltonian_mechanics
Deriving_Hamilton's_equations 一節：
H = (Σ_i p_i q_i_dot ) - L

Hamiltonian mechanics是Lagrangian mechanics的延伸，本質是Newtonian mechanics。

xianrenb 2022-3-24 10:53

[quote]原帖由 [i]xianrenb[/i] 於 2022-3-21 13:35 發表 [url=https://www.discuss.com.hk/redirect.php?goto=findpost&pid=546791960&ptid=30484421][img]https://www.discuss.com.hk/images/common/back.gif[/img][/url]

H = T + V

https://en.wikipedia.org/wiki/Hamiltonian_mechanics
Deriving_Hamilton's_equations 一節：
H = (Σ_i p_i q_i_dot ) - L

H = T + V

H = (Σ_i p_i q_i_dot ) - L

H = p q_dot - L
H = p q_dot - （T - V）
H = p q_dot - T + V
H = p v - T + V
H = p v - 1/2 m v^2 + V
H = m v v - 1/2 m v^2 + V
H = 1/2 m v^2 + V
H = T + V

Porky_Pig 2022-3-25 20:10

[quote]原帖由 [i]xianrenb[/i] 於 2022-3-24 10:53 發表 [url=https://www.discuss.com.hk/redirect.php?goto=findpost&pid=546886891&ptid=30484421][img]https://www.discuss.com.hk/images/common/back.gif[/img][/url]

H = T + V

H = (Σ_i p_i q_i_dot ) - L

H = p q_dot - L
H = p q_dot - （T - V）
H = p q_dot - T + V
H = p v - T + V
H = p v - 1/2 m v^2 + V
H = m v v - 1/2 m  ... [/quote]

xianrenb 2022-3-26 13:06

[quote]原帖由 [i]Porky_Pig[/i] 於 2022-3-25 20:10 發表 [url=https://www.discuss.com.hk/redirect.php?goto=findpost&pid=546938406&ptid=30484421][img]https://www.discuss.com.hk/images/common/back.gif[/img][/url]