Quantum Mechanical Operators

Each measurable parameter in a physical system is associated a quantum mechanical operator. Such operators arise because nature is being described in terms of waves via the use of wavefunctions rather than with discrete particles whose motion and dymamics can be described with the deterministic equations of Newtonian physics. Part of the development of quantum mechanics is the establishment of the operators associated with the parameters needed to describe the system. Some of those operators are listed below.

Symbol

Description

Operator

Any function of position, such as potential energy

- position operator

- position operator

- position operator

- component of momentum operator

- component of momentum operator

- component of momentum operator

Hat p

Total momentum operator

or

Time independent energy or hamiltonian operator

with natural extension to three dimensions.

Kinetic energy operator

with natural extension to three dimensions.

or

Time dependent energy or hamiltonian operator

x component of angular momentum

Or

y component of angular momentum

z component of angular momentum

Total angular momentum squared operator