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

            

a. Obtain an expression for E_nx, n_y in terms of n_x, n_y, a, and b by substituting this wave function into the two dimensional analog 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.

Transcribed Image Text:

Wn,n, (x, y) = Nsin- n,ty плх sin- 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0.1 0.2 0.3 0.4 0.5 0.1 0.2 0.3 0.4 0.5 (a) (b) 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0.1 0.2 0.3 0.4 0.5 0.1 0.2 0.3 0.4 0.5 (c) (d) 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 пm 0.1 0.2 0.3 0.4 0.5 0.1 0.2 0.3 0.4 0.5 (e) (f) TшTшT