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.

Since you have not included the experiment situation and the data, of course, i can not give you specific details about it. but i can you with this question.1) i will assume that the motion is projectile (parabolic) motion.2) yes, the horizontal distance depends on the horizontal velocity as, naming vx the horizontal velocity and t the time, it is: x = vx × t3) now, observe that the flight time depends on the vertical velocity as, naming voy the initial vertical velocity, t the time and y the vertical distance before reaching the ground: y = yo + voy×t - gt² / 2.the higher the initial vertical velocity (voy) the longer the object will be flying and so t will be higher in the equation for the horizontal distance.that explains the relationship between the horizontal distance and the horizontal velocity.