PPT - Heisenberg Uncertainty Principle - Civil Engineering (CE) PDF Download

 Page 1


Ch 28
1
Two Approaches to Quantum Mechanics
Schrödinger Wave Equation: is a “wave” equation
similar to the equations that describe other waves
Heisenberg Method: based on matrices.  We will only
study one part- the Heisenberg Uncertainty Principle
It was soon realized that the two methods gave
equivalent results
Modern quantum mechanics includes elements of both.
Correspondence Principle: required that a new theory
must be able to produce the old classical laws when
applied to macroscopic phenomena.
Page 2


Ch 28
1
Two Approaches to Quantum Mechanics
Schrödinger Wave Equation: is a “wave” equation
similar to the equations that describe other waves
Heisenberg Method: based on matrices.  We will only
study one part- the Heisenberg Uncertainty Principle
It was soon realized that the two methods gave
equivalent results
Modern quantum mechanics includes elements of both.
Correspondence Principle: required that a new theory
must be able to produce the old classical laws when
applied to macroscopic phenomena.
Ch 28
2
Heisenberg Uncertainty Principle
Consider the problem of trying to “see” an electron with a
photon
We will refer to the uncertainty in x as Dx
If l is the wavelength of the light then from diffraction:
l » D x
Photons have momentum p=h / l and
when the photon strikes the electron it
can give some or all of its momentum
to the electron
l
h
p » D
the product of these two is
h
h
p x » » D D
l
l ) )( (
Page 3


Ch 28
1
Two Approaches to Quantum Mechanics
Schrödinger Wave Equation: is a “wave” equation
similar to the equations that describe other waves
Heisenberg Method: based on matrices.  We will only
study one part- the Heisenberg Uncertainty Principle
It was soon realized that the two methods gave
equivalent results
Modern quantum mechanics includes elements of both.
Correspondence Principle: required that a new theory
must be able to produce the old classical laws when
applied to macroscopic phenomena.
Ch 28
2
Heisenberg Uncertainty Principle
Consider the problem of trying to “see” an electron with a
photon
We will refer to the uncertainty in x as Dx
If l is the wavelength of the light then from diffraction:
l » D x
Photons have momentum p=h / l and
when the photon strikes the electron it
can give some or all of its momentum
to the electron
l
h
p » D
the product of these two is
h
h
p x » » D D
l
l ) )( (
Ch 28
3
Heisenberg Uncertainty Principle
p 2
) )( (
h
p x ³ D D
A more careful analysis of this gives
p 2
h
t E ³ D D ) )( (
There is also an uncertainty principle for energy and time
Page 4


Ch 28
1
Two Approaches to Quantum Mechanics
Schrödinger Wave Equation: is a “wave” equation
similar to the equations that describe other waves
Heisenberg Method: based on matrices.  We will only
study one part- the Heisenberg Uncertainty Principle
It was soon realized that the two methods gave
equivalent results
Modern quantum mechanics includes elements of both.
Correspondence Principle: required that a new theory
must be able to produce the old classical laws when
applied to macroscopic phenomena.
Ch 28
2
Heisenberg Uncertainty Principle
Consider the problem of trying to “see” an electron with a
photon
We will refer to the uncertainty in x as Dx
If l is the wavelength of the light then from diffraction:
l » D x
Photons have momentum p=h / l and
when the photon strikes the electron it
can give some or all of its momentum
to the electron
l
h
p » D
the product of these two is
h
h
p x » » D D
l
l ) )( (
Ch 28
3
Heisenberg Uncertainty Principle
p 2
) )( (
h
p x ³ D D
A more careful analysis of this gives
p 2
h
t E ³ D D ) )( (
There is also an uncertainty principle for energy and time
Ch 28
4
Example 28-1. The strong nuclear force has a range of about 1.5x10
-15
m. In 1935 Hideki
Yukawa predicted the existence of a particle named the pion (p) that somehow “carried” the
strong nuclear force. Assume this particle can be created because the uncertainty principle
allows non-conservation of energy by an amount ?E as long as the pion can move between
two nucleons in the nucleus in time ?t so that the uncertainty principle holds. Assume that the
pion  travels at approximately the speed of light and estimate the mass of the pion. (See page
896 in textbook)
p 2
h
t E » D D
c
d
t ~ D
2
c m
p
» DE
If the velocity of the pion is slightly  less than c, then it can travel the distance
d = 1.5x10
-15
m in the time ?t where
The rest mass energy of the pion is equal to the uncertainty in energy
Page 5


Ch 28
1
Two Approaches to Quantum Mechanics
Schrödinger Wave Equation: is a “wave” equation
similar to the equations that describe other waves
Heisenberg Method: based on matrices.  We will only
study one part- the Heisenberg Uncertainty Principle
It was soon realized that the two methods gave
equivalent results
Modern quantum mechanics includes elements of both.
Correspondence Principle: required that a new theory
must be able to produce the old classical laws when
applied to macroscopic phenomena.
Ch 28
2
Heisenberg Uncertainty Principle
Consider the problem of trying to “see” an electron with a
photon
We will refer to the uncertainty in x as Dx
If l is the wavelength of the light then from diffraction:
l » D x
Photons have momentum p=h / l and
when the photon strikes the electron it
can give some or all of its momentum
to the electron
l
h
p » D
the product of these two is
h
h
p x » » D D
l
l ) )( (
Ch 28
3
Heisenberg Uncertainty Principle
p 2
) )( (
h
p x ³ D D
A more careful analysis of this gives
p 2
h
t E ³ D D ) )( (
There is also an uncertainty principle for energy and time
Ch 28
4
Example 28-1. The strong nuclear force has a range of about 1.5x10
-15
m. In 1935 Hideki
Yukawa predicted the existence of a particle named the pion (p) that somehow “carried” the
strong nuclear force. Assume this particle can be created because the uncertainty principle
allows non-conservation of energy by an amount ?E as long as the pion can move between
two nucleons in the nucleus in time ?t so that the uncertainty principle holds. Assume that the
pion  travels at approximately the speed of light and estimate the mass of the pion. (See page
896 in textbook)
p 2
h
t E » D D
c
d
t ~ D
2
c m
p
» DE
If the velocity of the pion is slightly  less than c, then it can travel the distance
d = 1.5x10
-15
m in the time ?t where
The rest mass energy of the pion is equal to the uncertainty in energy
Ch 28
5
Example 28-1 (continued). The strong nuclear force has a range of about 1.5x10
-15
m. In
1935 Hideki Yukawa predicted the existence of a particle named the pion (p) that somehow
“carried” the strong nuclear force. Assume this particle can be created because the uncertainty
principle allows non-conservation of energy by an amount ?E as long as the pion can move
between two nucleons in the nucleus in time ?t so that the uncertainty principle holds.
Assume that the pion  travels at approximately the speed of light and estimate the mass of the
pion. (See page 896 in textbook)
p 2
h
t E » D D
p
p
2
2
h
c
d
c m »
÷
ø
ö
ç
è
æ
d
hc
c m
p
p
2
2
»
) 10 5 . 1 ( 2
) / 10 3 )( 10 6 . 6 (
15
8 34
m
s m Js
-
-
´
´ ´
»
p
MeV J c m 130 10 1 . 2
11 2
» ´ »
-
p
A few years later the pion was discovered and it’s actual mass is  ˜ 140 MeV/c
2
.
We substitute the above expressions for ?E and ?t:
2
130
c
Mev
m »
p