This problem concerns the one-dimensional schrödinger equation with the harmonic oscillator potential u(x) = 2m00"x2. (a) calculate as a function of the variable z the hermite polynomial function h4(z). you can check your answer by looking it up on the internet, but use the formula with the nth derivative of exp(-z) to actually calculate your answer. (b) using your answer to part b, give an expression for the state y4(x), the n 4 solution to the time- out front can just be called a (c) show that your function in part c satisfies the time-independent schrödinger equation with e- hoo. in other words, put your function from part b into the time-independent schrödinger equation with e =-hoo, and show that it works.