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What used to be functions in the context of classical mechanics like position, linear momentum, angular momentum, etc in quantum mechanics are operators (these operators act on the state to get results). So the question is: Historically, conceptually, and mathematically how functions become operators in quantum mechanics?

Phyllipe
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  • Possible duplicate: http://physics.stackexchange.com/q/77275/ – Kyle Kanos Nov 14 '13 at 13:57
  • Note: operators do not act on the wave function. They act on a state. The result of the position operator acting on that state is the wave function. – Wouter Nov 14 '13 at 19:12
  • The result of the position operator acting on a state is not the wavefunction. The result of an eigenket of the position operator being projected onto a state is the wavefunction.

    Positions in the position basis operate perfectly well on wavefunctions.

     – lionelbrits Nov 14 '13 at 19:20
  • @lionelbrits Oops, good point. – Wouter Nov 14 '13 at 20:58

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