- Chapter 10, Problem 5 (page 372).
- Chapter 10, Problem 11 (page 373).
- Chapter 10, Problem 15 (page 373).
- Chapter 10, Problem 16 (page 373).
- Chapter 10, Problem 17 (page 373).
- 20 points extra credit: In Chapter 9 we discussed
the effect of Coulomb repulsion on the energy levels of the Helium
atom. Use Mathematica to calculate the Coulomb repulsion between
the electrons in the Helium atom for the following two configurations
(see Figure 9.7):
To carry out this calculation, use the following procedure:
- The ground state of Helium (n = 1, l = 0, n =
1, l = 0)
- The first excited state of Helium (n = 1, l =
0, n =
2, l = 0)
In order to receive the extra credit, you should create a Mathematica
Notebook, showing on the relevant calculations, and submit it electronically
to Prof. Wolfs at email@example.com. The
name of the file should be hw09p06XXYYYYYYYY.nb where XX are your initials
and YYYYYYYY is your student id number. The subject of the email
should start with hw09p06XXYYYYYYYY.
- Obtained the wavefunctions for each electron from Table 7.2.
- Construct the appropriate total wavefunction of the state with
the proper spatial symmetry.
- The position of electron 1 is specified by 3 spatial coordinates;
the position of electron 2 is specified by 3 other spatial coordinates. The
distance between the two electrons, Δr, depends on
these 6 spatial coordinates.
- To calculate the Coulomb repulsion, determine the expectation value
of 1/Δr. Note: this requires and integration
of over the 6 spatial coordinates.
Last updated on
Tuesday, January 17, 2012 7:01