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

most historians agree that gabriel mouton, the vicar of st. paul’s church in lyons, france, is the “founding father” of the metric system. he proposed a decimal system of measurement in 1670. mouton based it on the length of one minute of arc of a great circle of the earth (now called a nautical mile, 1852 meters). he also proposed the swing-length of a pendulum with a frequency of one beat per second as the unit of length (about 25 cm). a pendulum beating with this length would have been fairly easy to produce, thus facilitating the widespread distribution of uniform standards. over the years, his work was revised, improved, and extended by a number of french scientists.

the political sponsor of weights and measures reform in the french revolutionary national assembly was the bishop of autun, better known as talleyrand. under his auspices, the french academy appointed several committees to carry out the work of developing a usable system of weights and measures for france. one of the committees recommended a decimalized measurement system based upon a length equal to one ten-millionth of the length of a quadrant of the earth’s meridian (i.e., one ten-millionth of the distance between the equator and the north pole).