## 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 |