1. Quantum mechanics I Fall 2012
Physics 451
Quantum mechanics I
Fall 2012
Karine Chesnel

2. Monday Sep 3: NO CLASS (Holiday)
Phys 451
Announcements
Monday Sep 3: NO CLASS (Holiday)
Homework 1: Today Aug 31st by 7pm
Pb 1.1, 1.2, 1.3
Homework 2: Group presentations Sep 5th
Homework 3: F Sep 7th by 7pm
Pb 1.4, 1.5, 1.7, 1.8
Homework
Help sessions: T Th 3-6pm

3. Famous scientist who contributed to the foundation
Phys 451
Announcements
Next class Sep 5th
Group presentations
Will count as homework 2, 20 points plus 5 quiz points for presenting
Famous scientist who contributed to the foundation
of Quantum Mechanics
Einstein
Schrödinger
Planck
De Broglie
Heisenberg
Dirac
Pauli
Born
Bohr

4. Probabilities Quantum mechanics Discrete variables
Examples of discrete distributions:
Age pyramid
for a certain population
(Utah, 2000)
Distribution of scores
in a class

5. Probabilities Quantum mechanics Discrete variables
Example:
number of siblings
for each student
in the class
Distribution of the system
Probability for a given j:
Average value of j:
Average value of
a function of j
Average value
“Expectation” value

6. Quiz 2a What is the definition of the variance? A. B. C. D. E.
Quantum mechanics
Quiz 2a
What is the definition of the variance? A. B. C. D. E.

7. Probabilities Quantum mechanics Discrete variables The deviation:
Variance
The standard deviation

8. Distribution of scores
Quantum mechanics
Probabilities
Discrete variables
The variance defines how wide/narrow a distribution is
Spectral analysis
of a photograph
brightness
intensity
Narrow: small s
Wide: large s
Distribution of scores
in a class

9. Probabilities Quantum mechanics Continuous variables
The probability of finding
the particle in the segment dx
The density of probability:
Probability to find the particle
between positions a and b:
Normalization:

10. Probabilities Quantum mechanics Continuous variables Average values:
Variance:

11. Connection to Wave function
Quantum mechanics
Connection to
Wave function
Density of probability (now function of space and time):
Normalization:
Solutions have to be normalizable:
- needs to be square-integrable

12. Quiz 2b Is this wave function square integrable or not? A. YES B. NO
Quantum mechanics
Quiz 2b
Is this wave function square integrable or not?
A. YES
B. NO

13. Can Y stay normalized in time?
Quantum mechanics
Normalization of
Wave function
Normalization:
Can Y stay normalized in time?
If Y satisfies the Schrödinger equation and is normalizable, then indeed