The discussion revolves around finding the position operator \( x \) in the context of quantum mechanics, specifically when the momentum operator \( p \) is defined as \( (h/2m)^{1/2}(A+B) \) with the commutation relation \([A,B]=1\) and all other commutators being zero. Participants express confusion regarding the problem's requirements and the nature of operators in this context.
The discussion is ongoing, with participants sharing their confusion and seeking clarification. Some hints regarding the commutation relations have been provided, but there is no explicit consensus or resolution yet.
Participants note the challenge of interpreting the problem and the implications of the commutation relations in quantum mechanics. The nature of the operators and their definitions is a central point of inquiry.
qmpuzzler said:Homework Statement
I'm so confused about the question below,actually i cannot understand the problem at all.Could anybody help me out?Thank you
Homework Equations
Find the operator for position x if the operator for momentum p is taken to be (h/2m)½（A+B),with[A,B]=1,and all other commutators zero.
The Attempt at a Solution
i just cannot figure it out how can the position,which is a opeartor itself,can have a operator for.
mathfeel said:What is the commutation relation between x and p? How can you construct x to satisfy that commutation relation?
Diomarte said:QMPuzzler, just as a hint to what you were asked by the original helper, I think you might want to consider how the commutation relations work, for example: [x,p] = xp-px.