Operators in quantum mechanics
| Physical quantity | Operator |
|---|---|
| Position,x | $$x$$ |
| Linear momentum,p | $$-\iota\hbar \frac{\partial}{\partial x}$$ |
| Potential energy,V(x) | $$V(x)$$ |
| Kinetic energy,KE | $$-\frac{\hbar}{2m} \frac{\partial^2}{\partial x^2}$$ |
| Total energy,E | $$\iota\hbar \frac{\partial}{\partial t}$$ |
| Total energy (Hamiltonian),H | $$-\frac{\hbar}{2m} \frac{\partial^2}{\partial x^2} + V(x)$$ |
| Angular momentum,$$\hat{L_x}$$ | $$-\iota\hbar(y\frac{\partial}{\partial z}-z\frac{\partial}{\partial y})$$ |