In Franz Schwabl's QM book the idea of active transformation has been put in this way:(adsbygoogle = window.adsbygoogle || []).push({});

"transformation of a state Z to Z' and view Z' from the same reference frame".The statement follows by the argument that the state which arises through the transformation [tex]\Lambda^{-1}[/tex] is given as [tex]\psi\ '(\ x) =\psi\ (\Lambda^{-1}\ x)[/tex]

[tex]\psi\ (\ x)[/tex] has been actively moved from [tex]\ x [/tex] to [tex]\ x'[/tex] where [tex]\ x'=\Lambda^{-1}\ x[/tex].

That is, here x' denotes a point in the same reference gotten from [tex]\ x'=\Lambda^{-1}\ x[/tex]

In the same reference frame [tex]\psi\rightarrow\psi\ '[/tex]; But how can that [tex]\psi\ '(\ x)[/tex] be equal to [tex]\psi\ (\Lambda^{-1}\ x)[/tex]?

I know that active transformation is expressed in literature most commonly as [tex]\psi\ '(\ x) =\psi(\ x')[/tex],[as opposed to passive transformation [tex]\psi\ '(\ x') =\psi\ (\ x)[/tex]---here primed co-ordinate means a new primed co-ordinate system],however,I am struggling a bit with the definition...

**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!

# On the definition of Active Transformation

Loading...

Similar Threads - definition Active Transformation | Date |
---|---|

I Wave Functions of Definite Momentum | Oct 30, 2017 |

B Simple definition of spin? | Sep 13, 2016 |

Transformations of a vector in the active viewpoint | Nov 18, 2015 |

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