This preview shows pages 1–3. Sign up to view the full content.
PHYS126, L15: page 1 of 4
Lecture 15: Introduction to Quantum Mechanics
Shengwang Du, 28&30 March 2011
[Powerpoint slides: introduction]
1. Classical (Relativity) versus quantum way of thinking
Newtonian Mechanics:
Motion equation:
2
2
dt
r
d
m
a
m
F
r
r
r
=
=
Initial condition:
}
,
,
{
)
0
(
0
0
0
0
z
y
x
r
t
r
=
=
=
r
r
,
0
)
0
(
v
t
v
r
r
=
=
Relativistic Mechanics:
Motion equation:
⎟
⎠
⎞
⎜
⎝
⎛
=
=
dt
r
d
m
dt
d
dt
P
d
F
r
r
r
γ
Initial condition:
}
,
,
{
)
0
(
0
0
0
0
z
y
x
r
t
r
=
=
=
r
r
,
0
)
0
(
v
t
v
r
r
=
=
[Powerpoint slide]
In both Newtonian and Relativistic Mechanics, motion of an object is described by the
motion equation (governed by force) and initial values of position and velocity. In other
word, with the motion equation, you can precisely predict the future of an object if you
know its initial values of position and velocity. The state of a particle is described by its
displacement
)
(
t
r
r
and velocity
)
(
t
v
r
(or momentum):
State :
)
(
t
r
r
&
)
(
t
v
m
P
r
r
=
mg
r
0
,v
0
r
(t),
v
(t)
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentPHYS126, L15: page 2 of 4
Therefore, the Newtonian and relativistic mechanics depend on that the position and
momentum of an object can be determined simultaneously.
Question: What will happen if you are told by the creator that the position and
momentum can not be determined at the same time?
Quantum Mechanics
Heisenberg uncertainty relations
2
/
h
≥
Δ
Δ
p
x
[Beiser Ch 3 Eq. (3.21)]
In Quantum Mechanics, talking about
)
(
t
r
r
and
)
(
t
v
r
at the same time is meaningless. In
other word, Quantum Mechanics is not interested in talking bout an individual event
about
)
(
t
r
r
and
)
(
t
v
r
that is the main task of classical (relativistic) mechanics. Quantum
Mechanics does not intend to tell you the details of orbit
)
(
t
r
r
and velocity
)
(
t
v
r
of an
individual event in the time and space this is the most difficult thing for people to
understand because we always think about an object at some position with some velocity.
In Quantum Mechanics, the state of a given system (or a particle) is completely described
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '11
 HoBunCHAN
 Physics, Power

Click to edit the document details