**Problem Statement:**22. Define the operator \( \hat{B} = c\hat{x} + \hat{p} \) and \( \hat{A} = c\hat{x} - \hat{p} \). Calculate \( [\hat{A}, \hat{B}] \).---**Discussion:**The task is to calculate the commutator \([\hat{A}, \hat{B}]\) where:- \( \hat{B} = c\hat{x} + \hat{p} \)- \( \hat{A} = c\hat{x} - \hat{p} \)In quantum mechanics, the commutator \([ \hat{A}, \hat{B} ]\) is defined as:\[[\hat{A}, \hat{B}] = \hat{A} \hat{B} - \hat{B} \hat{A}\]With the provided definitions, you can proceed to explicitly calculate the commutator using the properties of operators \(\hat{x}\) (position operator) and \(\hat{p}\) (momentum operator), and their known commutation relation \( [\hat{x}, \hat{p}] = i\hbar \). This can include expansions and simplifications by collecting like terms, considering these operators' linearity and distributive properties.

In general the commutator of x and x is zero, p and p is also zero. The commutator of x and p is ih…

Answered: 22. Define the operator B = câ + p and…