Klein–Gordon hong-têng-sek

Klein–Gordon hong-têng-sek (Klein-Gordon equation) sī siong-tùi-lūn liōng-chú le̍k-ha̍k kap liōng-chú tiûⁿ-lūn tiong siōng ki-pún ê hong-têng-sek, i sī Schrödinger hong-têng-sek ê te̍k-sû siong-tùi-lūn hêng-sek, iōng-lâi biâu-su̍t spin 0 lia̍p-chú. Klein–Gordon hong-têng-sek sī Sūi-tián lí-lūn bu̍t-lí-ha̍k-ka Oskar Klein kap Tek-kok ê Walter Gordon tī 1920 nî-tāi kàu 1930 nî-tāi hun-pia̍t to̍k-li̍p thui-tō ·chhut-lâi ·ê.

Biâu-su̍t

Klein–Gordon hong-têng-sek sī án-ne:

${\frac {1}{c^{2}}}{\frac {\partial ^{2}}{\partial t^{2}}}\psi -\nabla ^{2}\psi +{\frac {m^{2}c^{2}}{\hbar ^{2}}}\psi =0$.

lán tiāⁿ-tiāⁿ ē ēng chū-jiân tan-ūi chè (c = <i id="mwGw">ħ</i> = 1) kā siá-chò

$-\partial _{t}^{2}\psi +\nabla ^{2}\psi =m^{2}\psi$

Kiōng-piàn hêng-sek

Chū-iû lia̍p-chú ê Schrödinger hong-têng-sek sī hui-siong-tùi-lūn liōng-chú le̍k-ha̍k siōng ki-pún ê hong-têng-sek:

${\frac {\mathbf {p} ^{2}}{2m}}\psi =i\hbar {\frac {\partial }{\partial t}}\psi$

kî-tiong $\mathbf {p} =-i\hbar \mathbf {\nabla }$ sī ūn-tōng-liōng soàn-hû.

Schrödinger hong-têng-sek tùi siong-tùi-lūn chi-hā m̄-sī kiōng-piàn, ì-sù tiō sī kóng i bōe boán-chiok Einstein ê te̍k-sû siong-tùi-lūn.

Lī-iōng te̍k-sû siong-tùi-lūn tiong sì-ūn-tōng-liōng ê put-piàn-sèng thui-tō ·chhut-lâi ê siong-tùi-lūn-sèng lêng-liōng ūn-tōng-liōng koan-hē

$E={\sqrt {\mathbf {p} ^{2}c^{2}+m^{2}c^{4}}}$

kā Schrödinger hong-têng-sek tò-chhiú-pêng chū-iû lia̍p chú ê tóng-lêng ${\frac {\mathbf {p} ^{2}}{2m}}$ ōaⁿ-tiāu,

chiong-kî-bóe tō ē tit-tio̍h i ê kiōng-piàn hêng-sek

$(\Box ^{2}+\mu ^{2})\psi =0,$

kî-tiong $\mu ={\frac {mc}{\hbar }}\,$

D'Alembertian sī $\Box ^{2}={\frac {1}{c^{2}}}{\frac {\partial ^{2}}{\partial t^{2}}}-\nabla ^{2}\,$

Koh khòaⁿ

• Dirac hong-têng-sek
• Liōng-chú tiûⁿ-lūn