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equations:schroedinger_equation [2020/04/10 11:44] 109.81.208.52 [Concrete] |
equations:schroedinger_equation [2020/11/21 01:43] (current) 2a01:cb15:33b:c600:f4a9:8015:b3fa:6b19 Typo in the Hamiltonian |
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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}$: | 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} | + | \begin{equation} \hat H \equiv - \frac{\hbar^2}{2m} \nabla^2 + \hat V \hat{=} \frac{\hat{p}^2}{2m} + \hat V. \end{equation} |
It is conventional to denote operators by an additional hat above the classical symbol. | It is conventional to denote operators by an additional hat above the classical symbol. |