Lutasin ang ihbargamma^mupartial_{mu}psi=mcpsi

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

I-solve ang c

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

Mga Hakbang sa Pagso-solve ng Linear Equation

Pagpalitin ang magkabilang panig para nasa kaliwang bahagi ang lahat ng variable na term.

$$mc\psi =iℏ\gamma ^{\mu }∂_{μ}\psi$$

Ang equation ay nasa standard form.

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

I-divide ang magkabilang dulo ng equation gamit ang m\psi .

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

Kapag na-divide gamit ang m\psi , ma-a-undo ang multiplication gamit ang m\psi .

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

I-divide ang iℏ\gamma ^{\mu }∂_{μ}\psi gamit ang m\psi .

$$c=\frac{iℏ∂_{μ}\gamma ^{\mu }}{m}$$

I-solve ang m

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

Mga Hakbang sa Pagso-solve ng Linear Equation

Pagpalitin ang magkabilang panig para nasa kaliwang bahagi ang lahat ng variable na term.

$$mc\psi =iℏ\gamma ^{\mu }∂_{μ}\psi$$

Ang equation ay nasa standard form.

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

I-divide ang magkabilang dulo ng equation gamit ang c\psi .

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

Kapag na-divide gamit ang c\psi , ma-a-undo ang multiplication gamit ang c\psi .

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

I-divide ang iℏ\gamma ^{\mu }∂_{μ}\psi gamit ang c\psi .

$$m=\frac{iℏ∂_{μ}\gamma ^{\mu }}{c}$$