Using your result from P15.17, how many energy levels does a particle of mass m in a two-dimensional box of edge length a have with E ≤ 29h2/8ma2 ? What is the degeneracy of each level?
Reference problem 15.17
For a particle in a two-dimensional box, the total
energy eigenfunctions are
a. Obtain an expression for Enx, ny in terms of nx, ny, 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 nx and ny for plots a–f.
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