Solve ihbargamma^mupartial_{mu}psi=mcpsi

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

Solve for c

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

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$mc\psi =iℏ\gamma ^{\mu }∂_{μ}\psi$$

The equation is in standard form.

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

Divide both sides by m\psi .

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

Dividing by m\psi undoes the multiplication by m\psi .

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

Divide iℏ\gamma ^{\mu }∂_{μ}\psi by m\psi .

$$c=\frac{iℏ∂_{μ}\gamma ^{\mu }}{m}$$

Solve for m

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

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$mc\psi =iℏ\gamma ^{\mu }∂_{μ}\psi$$

The equation is in standard form.

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

Divide both sides by c\psi .

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

Dividing by c\psi undoes the multiplication by c\psi .

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

Divide iℏ\gamma ^{\mu }∂_{μ}\psi by c\psi .

$$m=\frac{iℏ∂_{μ}\gamma ^{\mu }}{c}$$