0Introduction
IB Quantum Mechanics
0 Introduction
Quantum mechanics (QM) is a radical generalization of classical physics. Pro-
found new features of quantum mechanics include
(i)
Quantisation — Quantities such as energy are often restricted to a discrete
set of values, or appear in definite amounts , called quanta.
(ii)
Wave-particle duality — Classical concepts of particles and waves become
merged in quantum mechanics. They are different aspects of a single entity.
So an electron will no longer be thought of a “particle” but an entity that
has properties of both particles and waves.
(iii)
Probability and uncertainty — Predictions in quantum mechanics involve
probability in a fundamental way. This probability does not arise from our
lack of knowledge of the system, but is a genuine uncertainty in reality. In
particular, there are limits to what we can ask about a physical system,
even in principle. For example, the Heisenberg uncertainty principle entails
that we cannot accurately know both the position and momentum of a
particle.
Quantum mechanics also involves a new fundamental constant
h
or
~
=
h
2π
. The
dimension of this is
[h] = ML
2
T
−1
= [energy] × [time] = [position] ×[momentum].
We can think of this constant as representing the “strength” of quantum effects.
Despite having these new profound features, we expect to recover classical physics
when we take the limit ~ → 0.
Historically, there are a few experiments that led to the development of
quantum mechanics.