Physics 4605, Wave mechanics II Project No. 2 Due March 9, 2001 Numerical Solutions of the Radial Equation for Central Potentials
References
See problem 8.1 and 10.31.
Goals
To modify the program used in Project #1 to work for the radial equation of a 3D
Quiz 7
PHY 4605
Friday, March 3
Show as much work as possible. Each problem counts 10 points.
In class we showed that spin angular momentum states in the coupled representation
can be written as linear combinations of states in the uncoupled representatio
Quiz 6
PHY 4605
Friday, February 24
Each problem is worth 10 points. Please make your answers as complete as possible
to receive maximum credit.
1. An initially unpolarized beam of Ag atoms is passed through a Stern-Gerlach (SG)
apparatus with its magneti
Quiz 5
PHY 4605
Friday, February 17, 2006
1. Solve the eigenvalue equation,
3
2
a
b
2
2
=
a
b
In other words, determine the eigenvalues 1 and 2 and the associated eigenvectors.
Normalize the eigenvectors so that |a|2 + |b|2 = 1.
2. From the results of pro
Quiz 4
PHY 4605
Friday, February 3
Each problem worth 10 pts. Show as much work as possible for maximum credit.
1. A hydrogen atom at t=0 is in a superposition state,
| (t = 0) =
1
|100 +
3
1
|210 +
3
1
|300
3
a) Determine an expression for the time-depen
Quiz 3
PHY 4605
Friday, January 27
Each problem is worth 10 points
1. A hydrogen atom is in a state given by the real-space wave function,
1
1
i
(r, , ) = 100 210 300
3
3
3
where
Hnlm = En nlm
and En the energy eigenvalues of a hydrogenic atom with Z = 1
Quiz 2
PHY 4605
Friday, January 20
Each problem is worth 10 points. Please show as much work as possible for credit.
1. A dumbbell molecule (rigid rotor) is in a rotational state described by the wave
function
(, ) =
10
Y+
60
1 1
Y+
61
42
Y
60
a) Verify
Quiz 1
PHY 4605
Friday, January 13
Each problem is worth 10 points. Please show as much work as possible for credit.
1. Consider a system in a superposition of angular momentum states,
1
1
| >= |l = 1, m = 0 > + |l = 1, m = 1 >
2
2
Compute the following e
Summary of Quantum Solution for the Hydrogen Atom Physics 4605 Spring 2001 Prof. Brian Tonner
nlm = R ( r )Yl m ( , ) n = 1,2,3. l = 0,1,.n - 1 -l m l
a0 = Z R10 = a 0
3/ 2 2
e 2
En = -
Z 2e2 13.6eV =- 2 2a 0 n n2
Zr 2 exp - a 0 Zr Zr 2 - exp - 2a a0 0
Physics 4605 Wave Mechanics 2- Spring 2001 Homework #9 Due April 18, 2001 Problems 12.28, 12.29, 12.30, 12.31, 12.32, 12.53 Also: Read problem 12.50, and do the following as an Excel spreadsheet problem: Consider that the interacting spins can only have t
PHYSICS 4605 Spring 2001 Homework #4 Due February 12, 2001 Read Liboff 8.2, 8.3, 8.4, 8.5, 8.6, 8.7 Part I: Finish first project. Structure of Project Report: 1. State of problem 2. Solution using analytical methods. Use a model potential if necessary. 3.
PHYSICS 4605 Wave Mechanics II Spring 2001 Homework #3 (graded) Due Feb. 5, 2001 Read and absorb Liboff 7.2, 7.9, 7.10, 11.14, 8.2, 8.3, 8.4 Part I: Textbook problems Do problems in Liboff 7.16, 7.63, 7.64, 7.67, 7.68 Part II: Numerical problem (to be use
Physics 4605, Wave mechanics II Project No. 3 Due April 23, 2001 The He atom: Self-consistent field and multi-electron orbitals
References
See Liboff Section 13.10. You should plan on reading about the Hartree method or Hartree-Fock method in at least one
Quiz 9
PHY 4605
Friday, March 24
1. Consider two electrons which are conned to a two-dimensional box of edge-length
L. Write the appropriate Hamiltonian for the system which includes kinetic energy
and electron-electron interaction.
2. Neglecting the elec