“‘Quantum mechanics’ is the description of the behavior of matter and light in all its details and, in particular, of the happenings on an atomic scale Things on a very small scale behave like nothing[.]
Trang 1“‘Quantum mechanics’ is the description
of the behavior of matter and light in all its details and, in particular, of the
happenings on an atomic scale Things on
a very small scale behave like nothing
that you have any direct experience
about They do not behave like waves,
they do not behave like particles, they do not behave like clouds, or billiard balls, or weights on springs, or like anything that you have ever seen.”
Richard P Feynman
Trang 3Lecture 6: Introduction to
Quantum Physics:
Matter Waves and the Schrödinger Equation
Trang 4 Electron Diffraction particles as waves
Matter-wave Interference
Composite particles
Electron microscopy
Heisenberg Uncertainty Principle
Schrödinger Equation (SEQ)
Time-independent SEQ gives static solutions for wavefunctions
Physical interpretation of the wavefunction
Trang 5electron gun
Ni Crystal
detector
q
In 1927-8, it was shown
(Davisson-Germer) that, like x-rays, ELECTRONS
can also diffract off crystals !
q
Interference peak !
Electrons can act like waves!!
What does this mean?
In discussion section:
q
Matter Waves
DeBroglie (1924) proposed that, like
photons, particles have a wavelength:
l = h/p Inversely proportional to
momentum.
• We will see later that the discrete
atomic emission lines also arise from
the wavelike properties of the
electrons in the field of the nucleus:
Atomic
hydrogen
Trang 6“Double-slit” Experiment for Electrons
Electrons are accelerated to
50 keV l = 0.0055 nm
Central wire is positively
charged bends electron
paths so they overlap
A position-sensitive detector
records where they appear.
<< 1 electron in system at
any time
[A TONOMURA (Hitachi) pioneered electron holography]
Trang 7Exercise 1: Matter wavelengths
What size wavelengths are we talking about? Consider a photon with energy 3 eV, and therefore momentum p = 3 eV/c Its wavelength is:
a) le = lp b) le < lp c) le > lp
What is the wavelength of an electron with the same momentum?
c eV
s eV
p
h
414 10
3 10
4
1 3
10 14
l
Trang 8 What size wavelengths are we talking about? Consider a photon with energy 3 eV, and therefore momentum p = 3 eV/c Its wavelength is:
a) le = lp b) le < lp c) le > lp
What is the wavelength of an electron with the same momentum?
le = h/pe Same relation for
particles and photons.
Compared to the energy of the photon (given above): E pc 3 eV
Note that the kinetic energy of the electron is different from the energy of the photon with the same momentum (and wavelength):
eV
eV / J
J
)
m )(
kg
(
s J
m
h m
p KE
6 19
24 2
9 31
2 34
2
2 2
10 8
8 10
602 1
10 41
1 10
414 10
11 9 2
10 625 6
2 2
l
s m / s nm
c eV
s eV
p
h
414 10
3 10
4
1 3
10 14
l
Exrcise 1: Matter wavelengths
Trang 9 The DeBroglie wavelength of an electron is inversely related
to the electron momentum:
Wavelength of an Electron
l = h/p
Frequently we need to know the relation between the
electron’s wavelength l and its kinetic energy E
p and E are related through the classical formula:
2
-31 e
2
-15 2
p
2m h
2m
l
nm eV
E
2
2
505 1
l
l in nanometers
l
nm eV
E photon 1240
p = h/l
For m = me:
(electrons)
always true!
Trang 10Interference of larger particles
Matter-wave interference has now been demonstrated with electrons, neutrons, atoms, small molecules, BIG molecules, & biological molecules
Recent Example: Interference of C 60 , a.k.a “fullerenes”, “buckyballs”
[A Zeilinger (U Vienna), 1999]
Mass = (60 C)(12 g/mole) = 1.2 x 10-24 kg 2
22
3
p
K E kT p kTm kg m s m