Issolvi (igamma_{mu}partial^mu-m)psi=0

$$( i \gamma _ { \mu } \partial ^ { \mu } - m ) \psi = 0$$

Solvi għal m

$$\left\{\begin{matrix}\\m=i\gamma _{μ}∂^{\mu }\text{, }&\text{unconditionally}\\m\in \mathrm{C}\text{, }&\psi =0\end{matrix}\right.$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Uża l-propjetà distributtiva biex timmultiplika i\gamma _{μ}∂^{\mu }-m b'\psi .

$$i\gamma _{μ}∂^{\mu }\psi -m\psi =0$$

Naqqas i\gamma _{μ}∂^{\mu }\psi miż-żewġ naħat. Xi ħaġa mnaqqsa minn żero tagħti numru negattiv.

$$-m\psi =-i\gamma _{μ}∂^{\mu }\psi$$

L-ekwazzjoni hija f'forma standard.

$$\left(-\psi \right)m=-i\gamma _{μ}\psi ∂^{\mu }$$

Iddividi ż-żewġ naħat b'-\psi .

$$\frac{\left(-\psi \right)m}{-\psi }=-\frac{i\gamma _{μ}\psi ∂^{\mu }}{-\psi }$$

Meta tiddividi b'-\psi titneħħa l-multiplikazzjoni b'-\psi .

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

Iddividi -i\gamma _{μ}∂^{\mu }\psi b'-\psi .

$$m=i\gamma _{μ}∂^{\mu }$$

Solvi għal γ_μ

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

Passi biex Issolvi l-Ekwazzjoni Lineari

Uża l-propjetà distributtiva biex timmultiplika i\gamma _{μ}∂^{\mu }-m b'\psi .

$$i\gamma _{μ}∂^{\mu }\psi -m\psi =0$$

Żid m\psi maż-żewġ naħat. Xi ħaġa plus żero jirriżulta f'dan in-numru stess.

$$i\gamma _{μ}∂^{\mu }\psi =m\psi$$

L-ekwazzjoni hija f'forma standard.

$$i\psi ∂^{\mu }\gamma _{μ}=m\psi$$

Iddividi ż-żewġ naħat b'i∂^{\mu }\psi .

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

Meta tiddividi b'i∂^{\mu }\psi titneħħa l-multiplikazzjoni b'i∂^{\mu }\psi .

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

Iddividi m\psi b'i∂^{\mu }\psi .

$$\gamma _{μ}=-\frac{im}{∂^{\mu }}$$