Consider the following equation: Yn (x) = by plotting the difference where n=0,1,.... and Ho(x) =1,...

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Consider the following equation: Yn (x) = by plotting the difference where n=0,1,.... and Ho(x) =1, and H₂(x) = 2x (a) Using python, make a plot of Un(x) for n = 0 and 1 on the same graph, in the range x = -8 to x = 8, with 200 points. (b) Using python, make a plot of the local kinetic energy - -n(x) on the same range. Use 'h' corresponding to the interval between the points from the above question (a). [See the note at the end for using 'h'] (c) Using python, verify that the following equation is properly satisfied at each point in the range, for each of these Un(x): 1 e √2"n! √√π -x²/2 H₂(x), [-21²2²2 + 12x²] #n(x) = En4u (x) dx² An (x) = [-²21/2²2 +22² - En] (x) 1 +=x²² dx² df dx where E₁ = 0.5 + n. Try smaller values of h to see how small you can get A₁, and comment on what limits the precision attainable. Note: For differentiation, use the following approximation: = f(x+h)-f(x - h) 2h Consider the following equation: Yn (x) = by plotting the difference where n=0,1,.... and Ho(x) =1, and H₂(x) = 2x (a) Using python, make a plot of Un(x) for n = 0 and 1 on the same graph, in the range x = -8 to x = 8, with 200 points. (b) Using python, make a plot of the local kinetic energy - -n(x) on the same range. Use 'h' corresponding to the interval between the points from the above question (a). [See the note at the end for using 'h'] (c) Using python, verify that the following equation is properly satisfied at each point in the range, for each of these Un(x): 1 e √2"n! √√π -x²/2 H₂(x), [-21²2²2 + 12x²] #n(x) = En4u (x) dx² An (x) = [-²21/2²2 +22² - En] (x) 1 +=x²² dx² df dx where E₁ = 0.5 + n. Try smaller values of h to see how small you can get A₁, and comment on what limits the precision attainable. Note: For differentiation, use the following approximation: = f(x+h)-f(x - h) 2h

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Step 12 Solution step 1 a The code is given below import numpy as np import matplotlibpyplot as plt from numpypolynomialhermite import hermval Part a k 200 number of intervals in the domain x h nplins... View the full answer