91影视

A differential equation that describes matter in quantum mechanics in terms of the wave-like properties of particles in a field. Its answer is related to a particle's probability density in space and time.

$\mathrm{唯}\left(\mathrm{x}\right)=\sqrt{\frac{\mathrm{尘伪}}{\mathrm{h}}}\text{鈥�}{\mathrm{e}}^{鈭�\frac{\mathrm{尘伪x}}{{\mathrm{h}}^2}}$when $\mathrm{x}鈮�0$

$\mathrm{唯}\left(\mathrm{x}\right)=\sqrt{\frac{\mathrm{尘伪}}{\mathrm{h}}}\text{鈥�}{\mathrm{e}}^{\frac{\mathrm{尘伪x}}{{\mathrm{h}}^2}}$ when$\mathrm{x}鈮�0$

$\mathrm{x}=\underset{鈭�\mathrm{鈭�}}{\overset{\mathrm{鈭�}}{鈭�}}{\mathrm{虫唯}}^2\mathrm{dx}=0$

${\mathrm{x}}^2=\underset{鈭�\mathrm{鈭�}}{\overset{\mathrm{鈭�}}{鈭�}}{\mathrm{x}}^2{\mathrm{唯}}^2\mathrm{dx}=\frac{2\mathrm{尘伪}}{{\mathrm{h}}^2}\underset{0}{\overset{\mathrm{鈭�}}{鈭�}}{\mathrm{x}}^2{\mathrm{e}}^{鈭�\frac{2\mathrm{尘伪}}{{\mathrm{h}}^2}}\mathrm{dx}$

$\mathrm{x}=\frac{{\mathrm{h}}^4}{2{\mathrm{m}}^2{\mathrm{伪}}^2}$

${\mathrm{蟽}}_{\mathrm{x}}=\frac{{\mathrm{h}}^2}{\sqrt{2}\mathrm{尘伪}}$

$\frac{\mathrm{诲唯}}{\mathrm{dx}}=鈭�\frac{\mathrm{尘伪}}{{\mathrm{h}}^2}{\mathrm{e}}^{\frac{鈭�\mathrm{尘伪x}}{{\mathrm{h}}^2}}$ for $x鈮�0$

$\frac{\mathrm{诲唯}}{\mathrm{dx}}=鈭�\frac{\mathrm{尘伪}}{{\mathrm{h}}^2}{\mathrm{e}}^{\frac{\mathrm{尘伪x}}{{\mathrm{h}}^2}}$ for $\mathrm{x}鈮�0$

$\frac{\mathrm{诲唯}}{\mathrm{dx}}={\left(\frac{\sqrt{\mathrm{尘伪}}}{\mathrm{h}}\right)}^3\left[鈭�\mathrm{胃}\left(\mathrm{x}\right){\mathrm{e}}^{\frac{鈭�\mathrm{尘伪x}}{{\mathrm{h}}^2}}+\mathrm{胃}(鈭�\mathrm{x}){\mathrm{e}}^{\frac{\mathrm{尘伪x}}{{\mathrm{h}}^2}}\right]$

$\frac{{\mathrm{d}}^2\mathrm{唯}}{{\mathrm{dx}}^2}={\left(\frac{\sqrt{\mathrm{尘伪}}}{\mathrm{h}}\right)}^3\left[鈭�\mathrm{未}\left(\mathrm{x}\right){\mathrm{e}}^{\frac{鈭�\mathrm{尘伪x}}{{\mathrm{h}}^2}}+\frac{\mathrm{尘伪}}{{\mathrm{h}}^2}\mathrm{胃}\left(\mathrm{x}\right){\mathrm{e}}^{\frac{鈭�\mathrm{尘伪x}}{{\mathrm{h}}^2}}鈭�\mathrm{未}(鈭�\mathrm{x}){\mathrm{e}}^{\frac{\mathrm{尘伪x}}{{\mathrm{h}}^2}}+\frac{\mathrm{尘伪}}{{\mathrm{h}}^2}\mathrm{胃}(鈭�\mathrm{x}){\mathrm{e}}^{\frac{\mathrm{尘伪x}}{{\mathrm{h}}^2}}\right]$

Here,

$\mathrm{未}(鈭�\mathrm{x})=\mathrm{未}\left(\mathrm{x}\right)$,

$\mathrm{f}\left(\mathrm{x}\right)\mathrm{未}\left(\mathrm{x}\right)=\mathrm{f}\left(0\right)\mathrm{未}\left(\mathrm{x}\right)$

$\mathrm{胃}(鈭�\mathrm{x})+\mathrm{胃}\left(\mathrm{x}\right)=1$

$\frac{{\mathrm{d}}^2\mathrm{唯}}{{\mathrm{dx}}^2}={\left(\frac{\sqrt{\mathrm{尘伪}}}{\mathrm{h}}\right)}^3\left[鈭�2\mathrm{未}\left(\mathrm{x}\right)+\frac{\mathrm{尘伪}}{{\mathrm{h}}^2}{\mathrm{e}}^{\frac{鈭�\mathrm{尘伪x}}{{\mathrm{h}}^2}}\right]$

$\mathrm{p}=0$

$p^2=鈭�h^2\underset{鈭�\mathrm{鈭�}}{\overset{\mathrm{鈭�}}{鈭�}}唯\frac{d^2唯}{d{x}^2}dx$

$p^2=鈭�h^2{\left(\frac{\sqrt{m伪}}{h}\right)}^3\underset{鈭�\mathrm{鈭�}}{\overset{\mathrm{鈭�}}{鈭�}}{e}^{鈭�\frac{m伪x}{h^2}}\left[鈭�2未\left(x\right)+\frac{m伪}{h}{e}^{鈭�\frac{m伪x}{h^2}}\right]dx$

$p^2={\left(\frac{m伪}{h}\right)}^2\left[2鈭�2\frac{m伪}{h^2}\underset{0}{\overset{\mathrm{鈭�}}{鈭�}}{e}^{鈭�\frac{2m伪}{h^2}}dx\right]$

$\begin{array}{c}{p}^2={\left(\frac{m伪}{h}\right)}^2\left[1鈭�\frac{m伪}{h^2}\frac{h^2}{2m伪}\right]\\ \text{鈥夆赌夆赌夆赌夆赌夆赌夆赌�}={\left(\frac{m伪}{h}\right)}^2\end{array}$

$p^2={\left(\frac{m伪}{h}\right)}^2$

${蟽}_p=\frac{m伪}{h}$

$\begin{array}{c}{蟽}_x{蟽}_p=\frac{h^2}{\sqrt{2}m伪}\frac{m伪}{h}\text{鈥�}\\ \text{鈥夆赌夆赌夆赌夆赌夆赌夆赌夆�夆�夆�夆�夆��}=\sqrt{2}\frac{h}{2}>\frac{h}{2}\end{array}$