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This may seem like a silly question but if we have an operator of the form [itex]aX+bP[/itex] where a and b are some numbers and X and P are the position and momentum operators, doesn't this violate the uncertainty principle. Isn't it sort of measuring position and momentum simulataneously?

I recently came across quadrature operators where [itex]a=cos\theta[/itex] and [itex]b=sin\theta[/itex]. So how is this consistent with the uncertainty principle?

Thank you.

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# Quadrature operator

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