Whakaoti i te ihbarfrac{partialpsi_{1}}{partialt}=mc^2psi_{1}

$$i \hbar \frac { \partial \psi _ { 1 } } { \partial t } = m c ^ { 2 } \psi _ { 1 }$$

Whakaoti mō c

$$\left\{\begin{matrix}\\c=0\text{, }&\text{unconditionally}\\c\in \mathrm{C}\text{, }&\psi _{1}=0\text{ or }m=0\end{matrix}\right.$$

Ngā Upane mā te Kimi Pūtakerua

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$mc^{2}\psi _{1}=iℏ\frac{\mathrm{d}(\psi _{1})}{\mathrm{d}t}$$

Mā te whakawehe ki te m\psi _{1} ka wetekia te whakareanga ki te m\psi _{1}.

$$c^{2}=\frac{0}{m\psi _{1}}$$

Whakawehe 0 ki te m\psi _{1}.

$$c^{2}=0$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$c=0 c=0$$

Kua oti te whārite te whakatau. He ōrite ngā whakatau.

$$c=0$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$mc^{2}\psi _{1}=iℏ\frac{\mathrm{d}(\psi _{1})}{\mathrm{d}t}$$

Tangohia te iℏ\frac{\mathrm{d}(\psi _{1})}{\mathrm{d}t} mai i ngā taha e rua.

$$mc^{2}\psi _{1}-iℏ\frac{\mathrm{d}(\psi _{1})}{\mathrm{d}t}=0$$

Whakaraupapatia anō ngā kīanga tau.

$$-iℏ\frac{\mathrm{d}(\psi _{1})}{\mathrm{d}t}+m\psi _{1}c^{2}=0$$

Ko ngā tikanga tātai pūrua pēnei i tēnei nā, me te kīanga tau x^{2} engari kāore he kīanga tau x, ka taea tonu te whakaoti mā te whakamahi i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ina tuhia ki te tānga ngahuru: ax^{2}+bx+c=0.

$$m\psi _{1}c^{2}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi m\psi _{1} mō a, 0 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}}}{2m\psi _{1}}$$

Tuhia te pūtakerua o te 0^{2}.

$$c=\frac{0±0}{2m\psi _{1}}$$

Whakareatia 2 ki te m\psi _{1}.

$$c=\frac{0}{2m\psi _{1}}$$

Whakawehe 0 ki te 2m\psi _{1}.

$$c=0$$

Whakaoti mō m

$$\left\{\begin{matrix}\\m=0\text{, }&\text{unconditionally}\\m\in \mathrm{C}\text{, }&\psi _{1}=0\text{ or }c=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$mc^{2}\psi _{1}=iℏ\frac{\mathrm{d}(\psi _{1})}{\mathrm{d}t}$$

He hanga arowhānui tō te whārite.

$$\psi _{1}c^{2}m=0$$

Whakawehe 0 ki te c^{2}\psi _{1}.

$$m=0$$