Download Aug 29 - BYU Physics and Astronomy

Physics 451
Quantum mechanics I
Fall 2012
Karine Chesnel
Homework
First Homework (#1):
pb 1.1, 1.2, 1.3
due Friday Aug 31st by 7pm
First help sessions:
Thursday Aug 30th
exceptionally from 4:30pm
Introduction to
Quantum mechanics
Some History
Until 20th century: Classical Newtonian Mechanics…
Newton’s second Law
ma   F
Kinetic energy
1
T  mv 2
2
Mechanical energy of the system
dp
F
dt
E  T V
Deterministic view:
All the parameters of one particle can be determined exactly at any given time
Introduction to
Quantum mechanics
Some History
Early 20th century: Some revolutionary ideas from bright minds…
Werner Heisenberg
1901-1976
Erwin Schrödinger
1887-1961
Wolfgang Pauli
1900- 1958
Uncertainty Principle
Schrödinger Equation
Pauli exclusion principle
Introduction to
Quantum mechanics
Essential ideas
1) Uncertainty principle:
Conjugates quantities of a particle (ex: position & momentum)
can not be known simultaneously within a certain accuracy limit
2) Quantization:
The measurement of a physical quantity in a confined system results in quanta
(the measured values are discrete)
3) Wave-particle duality:
All particles can be described as waves (travelling both in space and in time)
The state of the particle is given by a wave function  ( x, t )
4) Extrapolation to classical mechanics:
The laws of classical Newtonian mechanics are the extrapolation of the
laws of quantum mechanics for large systems with very large number of particles
I-clicker test
Quiz 1a
How many terms are in the Schrodinger equation?
A. 1
B. 2
C. 3
D. 4
Introduction to
Quantum mechanics
Schrödinger equation (1926)
2

2
i

V 
2
t
2m x
Erwin Schrödinger
1887-1961
Introduction to
Quantum mechanics
Schrödinger equation
2

2
i

V 
2
t
2m x
m
the mass of the particle
the Planck’s constant

h
 1.05 1034 Js
2
V
the potential in which the particle exists

the “wave function” of the particle
But what is the physical meaning of the wave function?
Introduction to
Quantum mechanics
Wave function
The wave function
 ( x, t )
represents the “state of the particle”
Born’s Statistical interpretation
 ( x, t )
2
probability of finding the particle at point x, at time t
b
  ( x, t )
a
2
probability of finding the particle between points a and b
at time t
Introduction to
Quantum mechanics
Indeterminacy
Quantum mechanics only offers a statistical interpretation
about the possible results of a measurement
• Realist Position
• Orthodox position
• Agnostic position
Introduction to
Quantum mechanics
The realist position
Where is it?
I can’t see!
Now i see…
It WAS there!
Introduction to
Quantum mechanics
I need
to look into
this cloud…
The orthodox position
I found it!
“ observation not only disturb what is to be measured, they produce it…”
Introduction to
Quantum mechanics
The agnostic position
NO measure
NO answer
No answer until we measure it
NOW,
I know!
“seeing is believing”
I-clicker test
Quiz 1b
And you? What is your position?
A. Realist
B. Orthodox
C. Agnostic
Introduction to
Quantum mechanics
The most commonly adopted position
• Realist Position
• Orthodox position
• Agnostic position
The wave function evolves
in a deterministic way
according to the Schrödinger equation
but the MEASURMENT
perturbs the wave function,
which then collapses to a spike
centered around the measured value
The mysterious impact of measuring…
Introduction to
Quantum mechanics
The principle of indeterminacy
… and the powerful act of measuring
“seeing is knowing”
A spiritual analogy…
Faith
"If ye have faith ye hope for things
which are not seen, but which are true" (Alma 32:21).
Faith is a principle of action and power.
Quantum mechanics
Probabilities
Discrete variables
Distribution of the system
Probability for a given j:
N ( j)
N ( j)
P( j ) 
N

Average value of j:
j   jP( j )
j 0
Average value of
a function of j
Average value

f ( j )   f ( j ) P( j )
j 0
“Expectation” value
Example:
number of siblings
for each student
in the class
Quantum mechanics
Probabilities
Discrete variables
j  j  j
The deviation:
j  0
Variance
   j   j  j
2
The standard deviation
2

2
j
2
 j
2
2