Quadrature operator

  • #1

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.

Answers and Replies

  • #2
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I don't understand, what has the new operator have to do with the uncertainty principle ? If b≠0 for a≠0 then the operator, call it A, is different than both X and P which enter the uncertainty principle...
  • #3
Sorry, I think I may have had a bit of a misconception there.

I thought that being an eigenstate of a linear combination of X and P meant that the state was an eigenstate of X and P separately as well. Now its obvious that this was wrong. Sorry about that. Thank you for replying dextercioby.