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

You know famous equation, [itex] \frac{d<A>}{dt} = <\frac{i}{\hbar}[\hat{H},\hat{A}] + \frac{\partial\hat{H}}{\partial t} >[/itex]

But liboff said if [itex] \frac{\partial \hat{A} }{\partial t} = 0 [/itex] then, [itex] \frac{d<\hat{A}>}{dt} = 0 [/itex]

this is the proof

[itex] \frac{d<A>}{dt} = \frac{i}{\hbar}<\varphi_{n}|[\hat{H},\hat{A}]\varphi_{n}> = \frac{i}{\hbar}<\varphi_{n}|(\hat{H}\hat{A}-\hat{A}\hat{H})\varphi_{n}> [/itex]

[itex]=\frac{i}{\hbar}(<\hat{H}\varphi_{n}|\hat{A}\varphi_{n}> - <\varphi|\hat{A}\hat{H}\varphi_{n}>) [/itex]

[itex] \frac{i}{\hbar}E_{n}(<\varphi_{n}|\hat{A}\varphi_{n}> - <\varphi_{n}|\hat{A}\varphi_{n}>) = 0 [/itex]

If it is right, we can conclude time deviation of expectation value of certain operator is zero if and only if corresponding operator is not depending on time, no matter what value of [H,A]

is!

is it right? i can't accept this theorm.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

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

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

# [Q]Time deviation of expectation value

Loading...

Similar Threads for deviation expectation value |
---|

I Measurement of the mean value of the number of photons? |

I Infinite or undefined standard deviation in HUP |

I Expectation value of energy in TISE |

I Help with an expectation value formula |

I The symmetry argument and expectation value |

**Physics Forums | Science Articles, Homework Help, Discussion**