Differences

This shows you the differences between two versions of the page.

--- equations:schroedinger_equation [2018/05/14 07:05]
jakobadmin [Concrete]
+++ equations:schroedinger_equation [2019/05/21 16:55]
michael remove duplicated line in free particle example
@@ Line 33: / Line 33: @@
 \begin{align}
-\text{ the classical momentum } p_i \ &\rightarrow \ i \partial_{x_i} \, .
+\text{ the classical momentum } p_i \ &\rightarrow \ {-i} \hbar \partial_{x_i} \, .
 \end{align}
-Formulated differently, the Hamiltonian operator is calculated from the classical energy $E= T +V$ by replacing the classical momentum $p_i$ with the momentum operator $ \hat{p}_i \equiv i \partial_{x_i}$:
+Formulated differently, the Hamiltonian operator is calculated from the classical energy $E= T +V$ by replacing the classical momentum $p_i$ with the momentum operator $ \hat{p}_i \equiv {-i} \hbar \partial_{x_i}$:
 \begin{equation} \hat H \equiv - \frac{\hbar^2}{2m} \Delta^2 + \hat V \hat{=} \frac{\hat{p}^2}{2m} + \hat V. \end{equation}
@@ Line 85: / Line 85: @@
 \begin{align}
 H  \psi(x)&= E\psi(x) \notag \\
-\frac{-\hbar \partial_x^2}{2m} \psi(x) &=E\psi(x) \notag \\
 \frac{-\hbar \partial_x^2}{2m} \psi(x) &=E\psi(x) \notag
 \end{align}