According to the QM postulates, when we measure momentum, we get an eigenvalue of the momentum operator and the system takes on a state that is the corresponding eigenket.(adsbygoogle = window.adsbygoogle || []).push({});

Now, as I understand it, the eigenkets of the momentum operator are all Dirac delta functions corresponding to plane waves. A particle whose state vector is like that has a uniform probability of being anywhere at all in the universe. My understanding from Shankar is that no system actually has a plane wave state vector, and that these are just devices for helping us calculate and think about simple systems.

Shankar (2nd ed. p138) seems to imply that the state immediately after we take a momentum measurement is a vector whose representation in the momentum space is a very sharply peaked Gaussian-style curve centred around the result that we got. The representation in the coordinate space is then a broader Gaussian.

The trouble is that interpretation doesn't seem consistent with the postulate, which says that the state changes to an eigenket of the momentum operator. No matter how narrow and sharply peaked the Gaussian, it is still not an eigenket of that operator.

How can this puzzle be resolved?

**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!

# What state does a particle take on when we measure its momentum?

Loading...

Similar Threads - state does particle | Date |
---|---|

B Does QM state that Space is made of nothing? | Aug 23, 2017 |

I What does the state vector mean? | Mar 31, 2017 |

Does exchange of identical particles lead to new state? | Aug 18, 2015 |

Does Gaussian function give bound states for a particle? | Jun 2, 2014 |

How does particle detection affect a coherent state? | Jan 7, 2014 |

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