In this calculation you will analyze the quantum behavior of a particle moving in the following potential energy well: Region 1: U(x) = 00 Region 2: U(x) = 0 OSXSL Region 3: U(x) = Uo LSxS 21 (Uo >0) Region 4: U(x) = 00 x > 21 Begin by sketching this potential energy well. Part A. First we will consider states of motion of the particle of energy E Vo. 1. Write down solutions for the wave function in each of the 4 regions. V1= W, = (use coefficients A and B) 3 = (use coefficients C and D) WA= 12 should be written in terms of the parameter & = (2mE/A?)1/2. 3 should be written in terms of the parameter k' = [2m(E - U.)/A]]1/2. 103 2. Apply the boundary condition on w at x = 0 to eliminate one of the coefficients A or B. (Which one will be eliminated depends on how you wrote Pz.) 3. Apply the boundary condition on w at x = 24 to eliminate one of the coefficients C or D. 4. Apply the boundary condition on w at x = L to express your remaining coefficient in 3 (either Cor D) in terms of your remaining coefficient in w2 (either A or B). 5. Your entire wave function in the region x = -co to x = too should now depend on only one coefficient (either A or B). Explain how the normalization condition allows you to determine this remaining coefficient. Don't carry out the calculation, just show how it can be done. 6. There is still one boundary condition you haven't yet applied - the condition on dy/dx at x = L. Explain how applying this boundary condition allows you to determine the energy E. Don't carry out the calculation, just show how it can be done.Part C. Now consider the probability to locate the particle using the wave functions of Part B. 1. What is the probability of finding the particle in each region (1, 2, 3, and 4)? Don't evaluate any mathematical expressions, just write them down as completely as you can. 2. How does the probability to find the particle in region 2 compare with the probability to find the particle in region 3? probability (2) > probability (3) probability (2) = probability (3) probability (2)