Operator

Functions that take Wave functions as inputs. An operator is generally indicated with a hat.

• Using operators: you can derive the Schrödinger Wave Equation, as it is equivalent

Measured Values

In any measurement of the observable for an operator , the only values that can ever be observed are the eigenvalues Eigenvalues satisfy

where is a constant and the value that’s measured.

Operators

Hamiltonian

For example the Time Independent Schrödinger Wave Equation using operators:

is called the Hamiltonian, which is an operator yielding the total energy (kinetic + potential) Also

The kinetic-energy operator

The potential-energy operator

just multiplication by

The position operator

just multiplication by

The momentum operator

The expectation value of the momentum

Angular Momentum Operator

Possible values of are functions of such that Disagrees with Bohr Model angular momentum. Implies Electron motion is more like a vibration than it is a planetary orbit. Also note that , and the and components are not observable, as they are not calculable, even though they exist. See Quantum Numbers. Except for , when so the x and y components are 0.

Total energy operator

The expectation value of the energy