Talk:Quantum Mechanics/Operators and Commutators

Schroedinger mistake
Hi, There's a mistake in SE, SE is a second order PDE and your hamiltonian operator has only first order differential... to cut a long story short. You have: $$ i \hbar \frac{\partial}{\partial t}\Psi = - \frac{\hbar^2}{2m} \frac{\partial}{\partial x} \Psi + V(x)\Psi $$ should be: $$ i \hbar \frac{\partial}{\partial t}\Psi = - \frac{\hbar^2}{2m} \frac{{\partial}^2}{{\partial x}^2} \Psi + V(x)\Psi $$ This error persists over the entire page. Dkronst 17:19, 8 September 2005 (UTC)


 * I think I got them all

Operator mistake
Also x has to be considered as an operator. It acts as multiplication with x:

$$ \hat x \Psi(x) = x \Psi(x) $$

This also extends to the potential energy V(x). It is a function of the position operator, and thus, it acts as multiplication with V(x) :

$$ V(\hat x) \Psi(x) = V(x) \Psi(x) $$

If one does not consider position operators here, the reader has no chance to understand the basic commutation rules for momentum and position operators.

IIIHIII (discuss • contribs) 17:14, 18 December 2016 (UTC)