The wave function, y(x), of an electron in a potential well of finite depth and width,...

 

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The wave function, y(x), of an electron in a potential well of finite depth and width, L, is given by w(x) = Aex for x ≤0 y(x) =F sin(kx) + G cos(kx) for 0≤x≤L y(x) = Be-C for x ≥ L a. Given F = G =5, k = 1, and C=2, determine A. b. What is w(0)? y(x) 8 7 6 in 5 a N 1 FIGURE 6.22 Homework Exercise 6.27c. c. Given w(L) = y(0), determine the values of L and B whether this wave function corresponds to the ground energy state (see Figure 6.22). d. Given y(L) = y(0), determine the values of L and B if this wave function cor- responds to the third lowest energy state. e. Use a spreadsheet program to graph the wave function from part (d) over the range-2 ≤ x ≤ (L+2). Indicate the location and value of L along the x-axis. The wave function, y(x), of an electron in a potential well of finite depth and width, L, is given by w(x) = Aex for x ≤0 y(x) =F sin(kx) + G cos(kx) for 0≤x≤L y(x) = Be-C for x ≥ L a. Given F = G =5, k = 1, and C=2, determine A. b. What is w(0)? y(x) 8 7 6 in 5 a N 1 FIGURE 6.22 Homework Exercise 6.27c. c. Given w(L) = y(0), determine the values of L and B whether this wave function corresponds to the ground energy state (see Figure 6.22). d. Given y(L) = y(0), determine the values of L and B if this wave function cor- responds to the third lowest energy state. e. Use a spreadsheet program to graph the wave function from part (d) over the range-2 ≤ x ≤ (L+2). Indicate the location and value of L along the x-axis.