why do fermions obey Pauli Exclusion but bosons obey inclusion We dont know why this division but quantum mechanics distinguishes them in the symmetry under exchange of the coordinates of identical ID: 592528
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Fermions vs. Bosons, continued
why do fermions obey Pauli Exclusion, but bosons obey “inclusion”?
We don’t know why this division, but quantum mechanics distinguishes
them in the symmetry under exchange of the coordinates of identical,
interacting particles.
P
1,2
fermi
=
-
fermi
P
1,2
bose
= +
bose
Simple example using an independent systems wave function for two particles
.
fermi
=
A(1)B(2) - A(2)B(1) = Slater determinant for any number of particles
bose
=
A(1)B(2) + A(2)B(1)Slide2
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Quantum Concepts
1. Planck 1905 Quantization of Energy
E = h
2. Einstein 1905 Particle Nature of Light
p = h/ 3. DeBroglie ~1920 Wave Nature of Particles = h/p4. Bohr ~1920 Quantization of L2 = l(l+1) (h/2)2 ; Angular Momentum Lz = m (h/2) 2L+1 m values from –L to +L 5. Heisenberg ~1925 Uncertainty Principle px x h
Who When What Equation
or:
“why the electron does not
fall into the nucleus”
i.e., the concept of
ZERO POINT ENERGYSlide3
3Slide4
4
Results of a
double-slit-experiment
performed by Dr. A.
Tonomura
showing the build-up of an interference pattern of single electrons. This is a 30 minute time exposure!(Provided with kind permission of Dr. AkiraTonomura.)Slide5
Results of a
double-slit-experiment
performed by Dr. A.
Tonomura
showing the build-up of an interference pattern of single electrons. Numbers of electrons are 10 (a), 200 (b), 6000 (c), 40000 (d), 140000 (e).(Provided with kind permission of Dr. AkiraTonomura.)Movies available at:http://www.hitachi.com/rd/research/em/movie.htmlElectron or photon interference is a single particle phenomenon! 5Slide6
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Time dependent Schr
ö
dinger Equation
It says by inspection that the
future of a quantum state is predicted, IF one knows the wavefunction at a given time. (we never do, except for very simple experiments)All (non-relativistic) dynamics in nature are in principle describedby this simple equation! Only limited by computer size and power.We will show later in this course that ALL KINETIC RATE CONSTANTSfor the rate: state 1 state 2 are proportional to |H
12|2i.e., the square of the Hamiltonian matrix element connecting states 1 and 2.
(for example, the rate of excitation is proportional to the electric dipole
transition moment squared.)Slide7
7
Below are videos of time dependent quantum computations of an electron
moving through single and double slits.
What is the solution?
Non E eigenstates all exhibit moving probability density!Slide8
8
A moving “particle” is described by a superposition of many sin and cos waves which constructively interfere to give a spherical Gaussian probability near a certain point but destructively interfere everywhere else.
The Gaussian “wave packet” moves according to the kinetic energy given by
the average frequency of the sin waves. This is how Newton’s Laws emerge
from quantum theory.
Time dependent Schrödinger Equation Applied to a moving SINGLE particleLarge single slitVery small single slit
This demonstrates very well the uncertaintyprinciple, and the generation of kinetic energy during the confinement while passing throughthe slit, resulting in large spreading of thewavefunction after emerging from slit. Slide9
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A moving “particle” is described by a superposition of a great many
sin and
cos
waves which constructively interfere to give a Gaussian
probability near a certain point but destructively interfere everywhere else. The Gaussian “wave packet” moves according to the kinetic energy given bythe average frequency of the sin waves. This is how Newton’s Laws emergefrom quantum theory. Slits CLOSE togetherSlide10
10
Slits FAR apartSlide11
11Slide12
12
http://www-
lpl.univ
-
paris13.fr
/icap2012/docs/Juffmann_poster.pdf http://www.youtube.com/watch?v=NUS6_S1KzC8 Slide13
13Slide14
14Slide15
15Slide16
16Slide17
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