Distribution functions: In this exercise we'll look at various distribution functions and gain some understanding of the properties of various states through the form of these distributions. You will be asked to plot various distribution functions, and therefore you should write a numerical code for calculating the Q and Wigner distributions ( P is not required since it's sometimes less regular), in whichever language you prefer. a. We've written in class the P distribution function of a number state, and used the optical equivalence theorem to obtain an expression for the expectation value of normallyordered operators using the P function. Calculate the expectation value of the number operator n^=a^†a^ for number states n= 0,n=1 and n=2 using the optical equivalence theorem of the P distribution (obviously you know what the answer should be)