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10 Nov 2019
We consider a particle in a two-dimensional square well with side a. The well lies in the (x - y) plane, as shown in the figure (the left panel shows a top-view of the well, and the right panel shows the well and particle in perspective.) Since the "motion" of the particle in the x direction is independent of its motion in the y direction, the spatial part of the wavefunction is separable. Thus, the generic wavefunction for the particle in the well is psi(x, y) = A sin nx pi x/a sin ny pi y/a, When more than one state corresponds to a particular energy, those states are said to be degenerate. Which states in the enumeration in part (c) are degenerate? (Write down their values of nx and ny and the corresponding energy.) The "degeneracy order" is the number of states corresponding to a particular energy. What is the degeneracy order for the states enumerated in part (c)? Enumerate all the possible combinations of nx and ny giving an energy of 50E0. What is the degeneracy order? How many antinodes appear in the probability distribution for each of these states?
We consider a particle in a two-dimensional square well with side a. The well lies in the (x - y) plane, as shown in the figure (the left panel shows a top-view of the well, and the right panel shows the well and particle in perspective.) Since the "motion" of the particle in the x direction is independent of its motion in the y direction, the spatial part of the wavefunction is separable. Thus, the generic wavefunction for the particle in the well is psi(x, y) = A sin nx pi x/a sin ny pi y/a, When more than one state corresponds to a particular energy, those states are said to be degenerate. Which states in the enumeration in part (c) are degenerate? (Write down their values of nx and ny and the corresponding energy.) The "degeneracy order" is the number of states corresponding to a particular energy. What is the degeneracy order for the states enumerated in part (c)? Enumerate all the possible combinations of nx and ny giving an energy of 50E0. What is the degeneracy order? How many antinodes appear in the probability distribution for each of these states?
Irving HeathcoteLv2
3 Nov 2019