Consider the contour plots of Problem P15.17. a. What are the most likely area or areas...

Consider the contour plots of Problem P15.17.

a. What are the most likely area or areas Δx Δy to find the particle for each of the eigenfunctions of depicted in plots a–f?

b. For the one-dimensional box, the nodes are points. What form do the nodes take for the two-dimensional box? Where are the nodes located in plots a–f? How many nodes are there in each contour plot?

Reference 15.17

For a particle in a two-dimensional box, the total

energy eigenfunctions are

a. Obtain an expression for En_x, n_y in terms of n_x, n_y, a, and b by substituting this wave function into the twodimensionalanalog of Equation (15.19).

b. Contour plots of several eigenfunctions are shown here. The x and y directions of the box lie along the horizontal and vertical directions, respectively. The amplitude has been displayed as a gradation in colors. Regions of positive and negative amplitude are indicated. Identify the values of the quantum numbers n_x and n_y for plots a–f.