Hi everyone,(adsbygoogle = window.adsbygoogle || []).push({});

I was just working on some problems regarding the mathematical formalism of QM, and while trying to finish a proof, I realized that I am not sure if the following fact is always true:

Suppose that we have two linear operators A and B acting over some vector space. Consider a state ket | [itex]\psi[/itex] >

I am wondering if

< [itex]\psi[/itex] | (A+B) | [itex]\psi[/itex] > = < [itex]\psi[/itex] | A | [itex]\psi[/itex] > + < [itex]\psi[/itex] | B | [itex]\psi[/itex] >

is always true?

I am thinking that it IS true.

My attempt at the problem, is of course to try and show that

(A+B) | [itex]\psi[/itex] > = A | [itex]\psi[/itex] > + B | [itex]\psi[/itex] >

But I am having trouble finding a definition which will confirm this to always be true.

I feel like I am completely overlooking something. Does any one have a helpful hint for me? ANy literature to point me to? My linear algebra books are failing me on this one, at first glance.

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Help on the expectation value of two added operators

Loading...

Similar Threads - Help expectation value | Date |
---|---|

A General quantum measurements | Jan 18, 2018 |

I Help with an expectation value formula | Sep 16, 2017 |

Why is there no help: momentum expectation value 2D particle in a box | Nov 28, 2013 |

Angular Momentum Expectation Values help for noobie | Nov 26, 2007 |

Help with expected value of non-hermitian operators | Jan 2, 2007 |

**Physics Forums - The Fusion of Science and Community**