Quantum Bound States Lab Learning Goals Visualize wave functions, probability densities, and energy levels for bound states in various potentials. Describe how multiple representations used for wave functions relate to one another. Explain what is and is not time-dependent for an energy eigen-state and a superposition state. Predict how the curvature and amplitude of the wave function and the spacing of the energy levels depends on the shape of the potential and the mass of the particle. General remarks about the simulation The simulation solves the 1D Schrodinger equation numerically in real time. The mass is set to the electron mass. The wave functions are not normalized. There is no option for an infinite square well potential, but you can approximate it by making the height of the finite well very large. 1. Square well (using One Well option) a. You’ll notice that you can’t adjust the total energy in this exercise. Why not? Answer: LAB Name Date 1
b. Describe the stationary-state wave function ? for different eigen-states and explain the variations in ? with total energy. Answer: c. Vary the potential depth. Describe the change in ? and the probability density ? *?. Explain the variations. Answer: d. Vary the width of the potential and describe the changes in ? or ? *?. Explain the variations. Answer: e. Chose two potential heights, one of which simulates an infinite well. Answer: f. Estimate the energy eigenvalues for 3 states and verify with the levels in the simulation. Complete the Table 1 below. Be sure to indicate all the necessary simulation inputs. Answer: g. Do the energies change with particle mass as you expect? Show it quantitatively for one of the settings above. Answer: h. How many eigen-states do you predict the delta function potential well has? Explain for a particular setting. Answer: i. Determine the expectation values for x, x2, p, and p2 for the second excited state. Answer: Table 1. 2. Asymmetric potential well LAB Name Date 2
a. Vary the…