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bikashkanungo

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This equation was concluded after stating that the linear operator iħ∂/∂qr satisfy the same commutation relations with the q’s and with each other as p’s do.

Next it is stated that(Dirac, p-92) “ This possibility enables us to see that the q’s must form a complete commuting set of observables since it means that any function of the q’s and p’s could be taken to be a function of q’s and iħ∂/∂q ‘ s and then could not commute with all the q’s unless it is a function of the q’s only.

I could not understand the above statement. Can anyone help me in the explanation of it ??

Also there is stated that ∂fr/∂qs =∂fs /∂qr showing that the functions fr are all of the form :

fr = ∂F/∂qr, where F is independent of r . How is this equation concluded ??