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Chapter 40: Q. 16 (page 1175)

The graph in FIGURE EX40.16 shows the potential-energy function U(x of a particle. Solution of the Schr枚dinger equation finds that the n=3 level has E3=0.5eVand that the n=6 level has E6=2.0eV.

a. Redraw this figure and add to it the energy lines for the n=3 and n=6 states.

b. Sketch the n=3 and n=6 wave functions. Show them as oscillating about the appropriate energy line.

Short Answer

Expert verified

(a) The 3 energy level of energy 0.5eV and 6 energy level of energy 2.30eV is shown in the figure.

(b)

Step by step solution

01

Step 1. Given information

(a) The third energy level of energy 0.5eVand 6 energy level of energy 2.0eVis shown in the figure.

02

Step 2. To sketch the n=3 and n=6 wave functions,

For n=3, the wave function has 3 antinodes and 2 nodes. As E3<Vafterx=1, then the function decays exponentially inside the classical forbidden region.

For n=6, the wave function has 6 antinodes and 5 nodes. As the kinetic energy is larger in the region0<x<1. Therefore the wave function will have shorter wave length and shorted amplitude. And in the region 2<x<3, the wave function will have larger wave length and large amplitude.

03

Step 3. The sketch

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