Usually wavefunctions and operators are expressed in terms of position, but we can also express them in momentum space. In this case, the functions and operators become a function of p, the momentum of the system. The momentum operator is then defined as p -p and the position operator is defined dp a) Is the function g(p) -ep an eigenfunction of the position operator?
b) Is the function g(p) an eigenfunction of the momentum operator? Show vour worK.
c) Evaluate the commutator [T, p] in momentum space by operating on a given function f(p), i. e. [T, P| f(p)
d) The functions qn (p) form a complete set of eigenfunctions of the momen- tum operator p. Prove that these functions are also eigenfunctions of the Hamiltonian expressed in momentum space, H 2m