Given the Hamiltonian $H(x,p)$ of a system. Is there always a coordinate transformation such that the new Hamiltonian is $K(x',p')=K(p')$?

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  • $\begingroup$ @Qmechanic- I am reading this paper( cds.cern.ch/record/529134/files/0112010.pdf). In page 8 second paragraph, the author tells that we can always come up with such a transformation. $\endgroup$ – Rahul Raju Pattar Jun 7 '19 at 8:38
  • $\begingroup$ I updated the answer. $\endgroup$ – Qmechanic Jun 7 '19 at 8:53
  • $\begingroup$ What could be the canonical transformations which make 1-D harmonic oscillator and anharmonic oscillator locally indistinguishable? $\endgroup$ – Rahul Raju Pattar Jun 21 '19 at 15:36
  • $\begingroup$ The HJ equation points to some elliptic integral... $\endgroup$ – Qmechanic Jun 21 '19 at 15:50

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