ihbarfrac{partialpsi_{1}}{partialt}=mc^2psi_{1} eching

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

c uchun yechish

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

Kvadrat ildizini topish bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

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

m\psi _{1} ga bo'lish m\psi _{1} ga ko'paytirishni bekor qiladi.

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

0 ni m\psi _{1} ga bo'lish.

$$c^{2}=0$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$c=0 c=0$$

Tenglama yechildi. Yechimlar bir xil.

$$c=0$$

Kvadrat tenglamalaridan foydalanish qoidalari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

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

Ikkala tarafdan iℏ\frac{\mathrm{d}(\psi _{1})}{\mathrm{d}t} ni ayirish.

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

Shartlarni qayta saralash.

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

Bu kabi kvadrat tenglamalarni x^{2} sharti bilan, biroq x shartisiz hamon kvadrat tenglamasidan foydalanib yechish mumkin, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ular standart formulaga solingandan so'ng: ax^{2}+bx+c=0.

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

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} m\psi _{1} ni a, 0 ni b va 0 ni c bilan almashtiring.

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

0^{2} ning kvadrat ildizini chiqarish.

$$c=\frac{0±0}{2m\psi _{1}}$$

2 ni m\psi _{1} marotabaga ko'paytirish.

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

0 ni 2m\psi _{1} ga bo'lish.

$$c=0$$

m uchun yechish

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

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

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

Tenglama standart shaklda.

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

0 ni c^{2}\psi _{1} ga bo'lish.

$$m=0$$