Issolvi -hbar^2/2mpartial^2psi/partialx^2+Upsi=Epsi

$$- \frac { \hbar ^ { 2 } } { 2 m } \frac { \partial ^ { 2 } \psi } { \partial x ^ { 2 } } + U \psi = E \psi$$

Solvi għal E

$$\left\{\begin{matrix}E=U\text{, }&\psi \neq 0\text{ and }m\neq 0\\E\in \mathrm{R}\text{, }&\psi =0\text{ and }m\neq 0\end{matrix}\right.$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Immultiplika ż-żewġ naħat tal-ekwazzjoni b'2m.

$$\left(-\frac{ℏ^{2}}{2m}\right)\frac{\mathrm{d}(\psi )}{\mathrm{d}x^{2}}\times 2m+U\psi \times 2m=E\psi \times 2m$$

Esprimi \left(-\frac{ℏ^{2}}{2m}\right)\frac{\mathrm{d}(\psi )}{\mathrm{d}x^{2}} bħala frazzjoni waħda.

$$\frac{-ℏ^{2}\frac{\mathrm{d}(\psi )}{\mathrm{d}x^{2}}}{2m}\times 2m+U\psi \times 2m=E\psi \times 2m$$

Esprimi \frac{-ℏ^{2}\frac{\mathrm{d}(\psi )}{\mathrm{d}x^{2}}}{2m}\times 2 bħala frazzjoni waħda.

$$\frac{-ℏ^{2}\frac{\mathrm{d}(\psi )}{\mathrm{d}x^{2}}\times 2}{2m}m+U\psi \times 2m=E\psi \times 2m$$

Annulla 2 fin-numeratur u d-denominatur.

$$\frac{-ℏ^{2}\frac{\mathrm{d}(\psi )}{\mathrm{d}x^{2}}}{m}m+U\psi \times 2m=E\psi \times 2m$$

Esprimi \frac{-ℏ^{2}\frac{\mathrm{d}(\psi )}{\mathrm{d}x^{2}}}{m}m bħala frazzjoni waħda.

$$\frac{-ℏ^{2}\frac{\mathrm{d}(\psi )}{\mathrm{d}x^{2}}m}{m}+U\psi \times 2m=E\psi \times 2m$$

Annulla m fin-numeratur u d-denominatur.

$$-ℏ^{2}\frac{\mathrm{d}(\psi )}{\mathrm{d}x^{2}}+U\psi \times 2m=E\psi \times 2m$$

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

$$E\psi \times 2m=-ℏ^{2}\frac{\mathrm{d}(\psi )}{\mathrm{d}x^{2}}+U\psi \times 2m$$

L-ekwazzjoni hija f'forma standard.

$$2m\psi E=2Um\psi$$

Iddividi ż-żewġ naħat b'2\psi m.

$$\frac{2m\psi E}{2m\psi }=\frac{2Um\psi }{2m\psi }$$

Meta tiddividi b'2\psi m titneħħa l-multiplikazzjoni b'2\psi m.

$$E=\frac{2Um\psi }{2m\psi }$$

Iddividi 2U\psi m b'2\psi m.

$$E=U$$

Solvi għal U

$$\left\{\begin{matrix}U=E\text{, }&\psi \neq 0\text{ and }m\neq 0\\U\in \mathrm{R}\text{, }&\psi =0\text{ and }m\neq 0\end{matrix}\right.$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Immultiplika ż-żewġ naħat tal-ekwazzjoni b'2m.

$$\left(-\frac{ℏ^{2}}{2m}\right)\frac{\mathrm{d}(\psi )}{\mathrm{d}x^{2}}\times 2m+U\psi \times 2m=E\psi \times 2m$$

Esprimi \left(-\frac{ℏ^{2}}{2m}\right)\frac{\mathrm{d}(\psi )}{\mathrm{d}x^{2}} bħala frazzjoni waħda.

$$\frac{-ℏ^{2}\frac{\mathrm{d}(\psi )}{\mathrm{d}x^{2}}}{2m}\times 2m+U\psi \times 2m=E\psi \times 2m$$

Esprimi \frac{-ℏ^{2}\frac{\mathrm{d}(\psi )}{\mathrm{d}x^{2}}}{2m}\times 2 bħala frazzjoni waħda.

$$\frac{-ℏ^{2}\frac{\mathrm{d}(\psi )}{\mathrm{d}x^{2}}\times 2}{2m}m+U\psi \times 2m=E\psi \times 2m$$

Annulla 2 fin-numeratur u d-denominatur.

$$\frac{-ℏ^{2}\frac{\mathrm{d}(\psi )}{\mathrm{d}x^{2}}}{m}m+U\psi \times 2m=E\psi \times 2m$$

Esprimi \frac{-ℏ^{2}\frac{\mathrm{d}(\psi )}{\mathrm{d}x^{2}}}{m}m bħala frazzjoni waħda.

$$\frac{-ℏ^{2}\frac{\mathrm{d}(\psi )}{\mathrm{d}x^{2}}m}{m}+U\psi \times 2m=E\psi \times 2m$$

Annulla m fin-numeratur u d-denominatur.

$$-ℏ^{2}\frac{\mathrm{d}(\psi )}{\mathrm{d}x^{2}}+U\psi \times 2m=E\psi \times 2m$$

Żid ℏ^{2}\frac{\mathrm{d}(\psi )}{\mathrm{d}x^{2}} maż-żewġ naħat.

$$U\psi \times 2m=E\psi \times 2m+ℏ^{2}\frac{\mathrm{d}(\psi )}{\mathrm{d}x^{2}}$$

L-ekwazzjoni hija f'forma standard.

$$2m\psi U=2Em\psi$$

Iddividi ż-żewġ naħat b'2\psi m.

$$\frac{2m\psi U}{2m\psi }=\frac{2Em\psi }{2m\psi }$$

Meta tiddividi b'2\psi m titneħħa l-multiplikazzjoni b'2\psi m.

$$U=\frac{2Em\psi }{2m\psi }$$

Iddividi 2E\psi m b'2\psi m.

$$U=E$$