Atrisiniet ihbargamma^mupartial_{mu}psi=mcpsi

$$i \hbar \gamma ^ { \mu } \partial _ { \mu } \psi = m c \psi$$

Atrast c

$$\left\{\begin{matrix}c=\frac{iℏ∂_{μ}\gamma ^{\mu }}{m}\text{, }&m\neq 0\\c\in \mathrm{C}\text{, }&\psi =0\text{ or }\left(ℏ=0\text{ and }m=0\right)\text{ or }\left(\gamma =0\text{ and }\mu \neq 0\text{ and }m=0\right)\text{ or }\left(∂_{μ}=0\text{ and }m=0\right)\end{matrix}\right,$$

Lineāra vienādojuma risināšanas darbības

Mainiet puses tā, lai visi mainīgie locekļi atrastos pa kreisi.

$$mc\psi =iℏ\gamma ^{\mu }∂_{μ}\psi$$

Vienādojums ir standarta formā.

$$m\psi c=i\psi ℏ∂_{μ}\gamma ^{\mu }$$

Daliet abas puses ar m\psi .

$$\frac{m\psi c}{m\psi }=\frac{i\psi ℏ∂_{μ}\gamma ^{\mu }}{m\psi }$$

Dalīšana ar m\psi atsauc reizināšanu ar m\psi .

$$c=\frac{i\psi ℏ∂_{μ}\gamma ^{\mu }}{m\psi }$$

Daliet iℏ\gamma ^{\mu }∂_{μ}\psi ar m\psi .

$$c=\frac{iℏ∂_{μ}\gamma ^{\mu }}{m}$$

Atrast m

$$\left\{\begin{matrix}m=\frac{iℏ∂_{μ}\gamma ^{\mu }}{c}\text{, }&c\neq 0\\m\in \mathrm{C}\text{, }&\psi =0\text{ or }\left(ℏ=0\text{ and }c=0\right)\text{ or }\left(\gamma =0\text{ and }\mu \neq 0\text{ and }c=0\right)\text{ or }\left(∂_{μ}=0\text{ and }c=0\right)\end{matrix}\right,$$

Lineāra vienādojuma risināšanas darbības

Mainiet puses tā, lai visi mainīgie locekļi atrastos pa kreisi.

$$mc\psi =iℏ\gamma ^{\mu }∂_{μ}\psi$$

Vienādojums ir standarta formā.

$$c\psi m=i\psi ℏ∂_{μ}\gamma ^{\mu }$$

Daliet abas puses ar c\psi .

$$\frac{c\psi m}{c\psi }=\frac{i\psi ℏ∂_{μ}\gamma ^{\mu }}{c\psi }$$

Dalīšana ar c\psi atsauc reizināšanu ar c\psi .

$$m=\frac{i\psi ℏ∂_{μ}\gamma ^{\mu }}{c\psi }$$

Daliet iℏ\gamma ^{\mu }∂_{μ}\psi ar c\psi .

$$m=\frac{iℏ∂_{μ}\gamma ^{\mu }}{c}$$