What Is the Position Operator x When Momentum p Is Defined as (h/2m)½(A+B)?

[qmpuzzler]

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]

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.

What is the commutation relation between x and p? How can you construct x to satisfy that commutation relation?

 

[qmpuzzler]

Here is the question:
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.

Honestly,i have no idea what is the meaning of the question.

 

[Diomarte]

What is the commutation relation between x and p? How can you construct x to satisfy that commutation relation?

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.

 

[qmpuzzler]

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.

Thanks,but still have no clue in solving.can you explain how to work it out?