Riješi ihbargamma^mupartial_{mu}psi=mcpsi

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

Izračunaj c

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

Koraci rješavanja linearne jednadžbe

Zamijenite strane tako da svi izrazi s nepoznanicama budu s lijeve strane.

$$mc\psi =iℏ\gamma ^{\mu }∂_{μ}\psi$$

Jednadžba je u standardnom obliku.

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

Podijelite obje strane sa m\psi .

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

Dijeljenjem s m\psi poništava se množenje s m\psi .

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

Podijelite iℏ\gamma ^{\mu }∂_{μ}\psi s m\psi .

$$c=\frac{iℏ∂_{μ}\gamma ^{\mu }}{m}$$

Izračunaj m

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

Koraci rješavanja linearne jednadžbe

Zamijenite strane tako da svi izrazi s nepoznanicama budu s lijeve strane.

$$mc\psi =iℏ\gamma ^{\mu }∂_{μ}\psi$$

Jednadžba je u standardnom obliku.

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

Podijelite obje strane sa c\psi .

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

Dijeljenjem s c\psi poništava se množenje s c\psi .

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

Podijelite iℏ\gamma ^{\mu }∂_{μ}\psi s c\psi .

$$m=\frac{iℏ∂_{μ}\gamma ^{\mu }}{c}$$