*Problem A particle of mass m is in the state ¥(x, 1) = Ae¯allmx² /h)+ir]. where A and a are positive real constants. (a) Find A. (b) For what potential energy function V (x) does V satisfy the Schrödinge equation? (c) Calculate the expectation values of x, x², p, and p². р, (d) Find Or and Is their product consistent with the uncertainty principle?

Electrons with a speed of 1.4×106 m/sm/s pass through a double-slit apparatus. Interference fringes are detected with a fringe spacing of 2.4 mmmm .     Part A What will the fringe spacing be if the electrons are replaced by neutrons with the same speed? Express your answer in micrometers.         ΔynΔyn = 1.30•10−6 μmμm   SubmitPrevious AnswersRequest Answer  Incorrect; Try Again; 4 attempts remaining Part B What speed must neutrons have to produce interference fringes with a fringe spacing of 2.4 mmmm ? Express your answer in meters per second.

Q1. Consider the finite square well potential shown in the following diagram: U(x) E>0 L The potential is given by: for xL| -U. for 0 0is incident on this region from the left. Using the plane A particle with energy wave approximation for the particle: a) Show that Y = Ae*+Be¬k* is a suitable general solution to the time-independent Schrödinger wave-equation (TISE) that applies in the region x L write down the four equations arising from the boundary conditions that apply at x=0 and x=L .

Q3: For a quantum harmonic oscillator in its ground state. Find: a) (x) b) (x²) с) Ох