1. Quantum mechanics I Fall 2012
Physics 451
Quantum mechanics I
Fall 2012
Sep 17, 2012
Karine Chesnel

2. Monday: Review- Practice test Plan to work on your selected problem
Quantum mechanics
Announcements
Homework this week:
Tuesday Sep 18 by 7pm:
HW # 6 pb 2.10, 2.11, 2.12, 2.13, 2.14
Thursday Sep 20 by 7pm:
HW # 7 pb 2.19, 2.20, 2.21, 2.22
Monday: Review- Practice test
Plan to work on your selected problem
with your group and prepare the solution
to be presented in class (~ 5 to 7 min)

3. No student assigned to the following transmitters
Quantum mechanics
No student assigned to the following transmitters
17A79020
1E71A9C6
Please register your i-clicker at the class website!

4. Harmonic oscillator Quantum mechanics Ch 2.3x
V(x)
Solving the Schrödinger equation:
Expressing the Hamiltonian
in terms of convenient operators: or

5. In this definition, the states
Quantum mechanics Ch 2.3
Harmonic oscillator
Ladder operators:
Raising operator:
Lowering operator:
In this definition, the states
are normalized

6. Quiz 8a Quantum mechanics What will be the final state of the particle
after applying this operator?
(ignore the coefficients)

7. Harmonic oscillator Quantum mechanics Ch 2.3 Stationary states
The ground state is given by the condition
Ground energy

8. Harmonic oscillator Pb 2.10 Quantum mechanics Ch 2.3 Stationary states
The stationary states are orthonormal
Hermite polynomials
Pb 2.10
Building and
Checking the orthogonality

9. Quantum mechanics Ch 2.3
Harmonic oscillator
Energy levels x
V(x)

10. Expressing x, p and H in terms of ladder operators:
Quantum mechanics Ch 2.3
Harmonic oscillator
Expressing x, p and H in terms of ladder operators:
Operator position
Operator momentum
Operator Hamiltonian

11. Harmonic oscillator Pb 2.11, 2.12 Quantum mechanics Ch 2.3x
V(x)
Expectation values
Pb 2.11, 2.12

12. Quiz 8b True False Pb 2.13 Quantum mechanics
Since the operators a+ and a- are shifting the stationary states
from one level to another,
and since the stationary states are all orthogonal,
the expectations values for x and p on any state will ALWAYS be zero!
True
False
Pb 2.13