This question concerns the outcome when operator valued functions act on an energy eigenstate. Given an eigenstate at t =0, say |Ej > , I have seen or inferred in some of the literature that the following applies :(adsbygoogle = window.adsbygoogle || []).push({});

exp(-iHt/h) |Ej > = exp(- iEj t/h) |Ej >

Where h = h-bar

Ej is energy eigenstate j

H is the Hamiltonian

I am unclear in particular why we can say that if we apply a function with an operator as the argument to this energy eigenstate, it will return the function with the eigenvalue as the argument times the energy eigenstate. (assuming I have inferred what is in the notes correctly)

Would this then be a general result for all functions or do only certain functions satisfy this relationship. (So for example would it be true for sin(H) instead of exp(-iHt/h) )?

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

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!

# Functions with operator valued arguments acting on eigenstates

Loading...

Similar Threads for Functions operator valued |
---|

I Find the energy from the graph of the wave function |

I Help with a partition function calculation |

I Help with partition function calculation |

I What does this equation for a free particle mean? |

I Kinetic and Potential energy operators commutation |

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