Operators in quantum mechanics

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,$$\hat{L_x}$$ $$-\iota\hbar(y\frac{\partial}{\partial z}-z\frac{\partial}{\partial y})$$