diff --git a/src/presentation/main.md b/src/presentation/main.md index eba7717..dbc7d47 100644 --- a/src/presentation/main.md +++ b/src/presentation/main.md @@ -449,3 +449,41 @@ + +---- + +### Das Doppelspaltexperiment + +$$ \Psi = \Psi_{lok}(x-\frac{d}{2}) + \Psi_{lok}(x+\frac{d}{2})$$ + +;$$ \Delta\alpha = 2*\pi*n \forall n \in \mathbb{Z} $$ + +;$$ \Psi_{lok} = +A*e^{-\frac{x^2}{4*\sigma_x^2+\frac{h^2*t^2}{16*\pi^2*m^2*\sigma_x^2}}}*\circlearrowleft(\frac{x^2}{\frac{16*\sigma_x^4*\pi*m}{h*t}+\frac{h*t}{\pi*m}}) +$$ + +;$$ \frac{(x+\frac{d}{2})^2}{\frac{16*\sigma_x^4*\pi*m}{h*t}+\frac{h*t}{\pi*m}} = +\frac{(x-\frac{d}{2})^2}{\frac{16*\sigma_x^4*\pi*m}{h*t}+\frac{h*t}{\pi*m}} + 2*\pi*n$$ + +;$$ \frac{x*d}{\frac{16*\sigma_x^4*\pi*m}{h*t}+\frac{h*t}{\pi*m}} = +\frac{-x*d}{\frac{16*\sigma_x^4*\pi*m}{h*t}+\frac{h*t}{\pi*m}} + 2*\pi*n$$ + +;$$ \frac{2*x*d}{\frac{16*\sigma_x^4*\pi*m}{h*t}+\frac{h*t}{\pi*m}} = 2*\pi*n$$ + +--- + +### Das Doppelspaltexperiment + +$$ \frac{2*x*d}{\frac{16*\sigma_x^4*\pi*m}{h*t}+\frac{h*t}{\pi*m}} = 2*\pi*n$$ +;$$ 2*x*d = 2*\pi*n * (\frac{16*\sigma_x^4*\pi*m}{h*t}+\frac{h*t}{\pi*m})$$ +;$$ x = \frac{\pi*n}{d} * (\frac{16*\sigma_x^4*\pi*m}{h*t}+\frac{h*t}{\pi*m})$$ + +--- + +### Das Doppelspaltexperiment + +$$ x = \frac{\pi*n}{d} * (\frac{16*\sigma_x^4*\pi*m}{h*t}+\frac{h*t}{\pi*m})$$ +;$$ \lim_{t\rightarrow \infty},v = \frac{s}{t} \Rightarrow t = \frac{s}{v} $$ +;$$ x = \frac{\pi*n}{d} * \frac{h*t}{\pi*m} = \frac{n*h*t}{d*m} = \frac{n*h*s}{d*m*v}$$ +;$$ \lambda = \frac{h}{p} = \frac{h}{m*v} $$ +;$$ x = \frac{n*s*\lambda}{d} $$