For a particle in a two-dimensional box, the total energy eigenfunctions are a. Obtai...

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.