Interesting problem: Suppose one has 2 hermitian operators, O1,O2 with distinct eigenvalues.(adsbygoogle = window.adsbygoogle || []).push({});

Say the first is the Hamiltonian. We measure the energy, get a value, say E_1. So the system

is in |1>. Suppose now that the second operator has the property to turn state 1 into state |2> and operating on |2> gives |1>

Hence if after having measured the energy to be E_1, we operate on the state with the second op, we get |2>. No uncertainty about the outcome.

So should not the uncertainity be 0?

So O2|1>=|2>,<1|O2|1>=0

O2**2|1>=O2|2>=|1>. So <1|O2**2|1>=<1|1>=1

But uncertainity is (<1|O2**2|1>-<1|O2|1>**2)=1, not 0.

**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!

# Uncertainity question

Loading...

Similar Threads - Uncertainity question | Date |
---|---|

I Why is the Uncertainty principle inherent to particles? | Feb 21, 2018 |

B Uncertainity relation | Jan 25, 2018 |

I Are the energy fluctuations in space real or virtual? | Jan 18, 2018 |

I Field operators and the uncertainty principle | Dec 23, 2017 |

I GRE related question in Quantum | Jan 30, 2017 |

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