Introduction to Quantum Mechanics I
Quiz 5
Name:
April 4, 2012
Using the 2 2 matrices,
x =
0 1
1 0
,
y =
0 i
i 0
,
z =
1 0
0 1
factor
.
1 + x
= ,
2
where and are two-component column and row vectors, respectively.
Write explicitly. What state of the spin-
Introduction to Quantum Mechanics 1
Quiz 3
Name:
March 14, 2012
Suppose that a system can be described either by measurements of property A, or of property B, or of property C. That is, knowing the value of
A = a , or of B = b , or of C = c fully species
Chapter 11
Position and Momentum
As we have seen, a unitary operator maintains the lengths of all vectors. A
simple example of a unitary operator consists in taking an orthonormal set of
vectors,
cfw_ a |, cfw_|a ,
a |a = (a , a ),
(11.1)
and rearranging
Chapter 1
The Failure of Classical
Mechanics
Classical mechanics, erected by Galileo and Newton, with enormous contributions from many others, is remarkably successful. It enables us to calculate
celestial motions to great accuracy, and triumphed in the p
Introduction to Quantum Mechanics I
Quiz 4
Name:
March 28, 2012
As 2 2 matrices, the matrices are
x =
0 1
1 0
,
y =
0 i
i 0
,
z =
1 0
0 1
.
Compute by matrix multiplication both x z and z x . Express the answers
in terms of matrices.
Solution:
x z =
z x =
Chapter 10
Time Evolution
So far, we have been discussing kinematicsthe description of a physical system.
We will have more to say about kinematics this semester and next. But now the
time has come to introduce dynamicshow a physical system evolves in tim
Introduction to Quantum Mechanics 1
Quiz 2
Name:
March 5, 2012
Using the properties of the symbols, compute
1 + z 1 + x 1 + z
2
2
2
and thereby determine p(+x, +z), the probability of nding x = +1 given
that the system was previously placed in the state z
Introduction to Quantum Mechanics 1
Quiz 1
Name:
February 29, 2012
Using
x y = y x = iz ,
evaluate
eix /2 y eix /2 .
What is the interpretation of this quantity? What is the physical signicance
of eix /2 ?
Solution: This represents a rotation about the x
Chapter 8
Developments
We have now constructed the basic framework of quantum mechanics. In this
chapter, we will introduce some secondary concepts that are important in practice.
8.1
Matrix elements
A general algebraic element, say one representing a phy
Chapter 5
Construction of Quantum
Mechanics
We are now going to develop the mathematical framework of quantum mechanics, which is tied fundamentally to the process of measurement. It is a symbolic
representation of experiment. We generalize from what is d
Chapter 6
Probabilities and vectors
Now we must learn how to extract probabilities from our measurement symbols.
Thus, suppose we consider two successive Stern-Gerlach experiments, one of
which measures (selects) a particular vlaue of z , z , and a second
Chapter 4
More About Spin
4.1
Higher Spins
We have been analyzing the results of the Stern-Gerlach experiment on the
simplest possible atoms, those with spin 1/2. The next simplest situation occurs,
for example, with O2 molecules, where the beam of molecu
Chapter 3
Uncertainty principle
Now it is Ampers hypotheis that the source of all magnetic elds is the motion
e
of charges. In particular, magnetic dipole moments arise from the circulation
of charge. Thus, there must be a relation between a mechanical pr
Chapter 7
Wavefunctions
The transformation function a |b tells how to go from one description (a
states) to another (b states)from one class of states to another. But we dont
have to think of all states in a class; we can talk of two states only:
b 2,
a 1
Chapter 2
The Stern-Gerlach
Experiment
Let us now talk about a particular property of an atom, called its magnetic
dipole moment. It is simplest to rst recall what an electric dipole moment is.
Consider an electrically neutral system consisting of two sep