Download - From Feynman’s Introduction
From Feynman’s Introduction
What I am going to tell you about is what we teach our physics
students in the third or fourth year of graduate school .....
..... I’m going to explain to you what the physicists are doing when
they are predicting how Nature will behave, but I’m not going to
teach you any tricks so you can do it efficiently. You will discover
that in order to make any reasonable predictions with this new
scheme of quantum electrodynamics, you would need to make a
awful lot of little arrows on a piece of paper. It takes seven years---
four undergraduate and three graduate---to train our physics
students to do that in a tricky, efficient way. That’s where we are
going to skip seven years of education in physics: By explaining
quantum electrodynamics to you in terms of what we are really doing, I hope you will be able to understand it better than do some
of the students.
There are only three basic actions:
A photon goes from one place and time to another place and time.
An electron goes from one place and time to another place and time.
An electron emits or absorbs a photon at a certain place and time.
All Photons Are Travelling Forward, Backward and Without Time! With v>c, v=c, and v<c!
Photons Travel From Place to Place
The Photons Scatter Inside withPrecisely the Same Total Amplitude as that Predicted by Maxwell’s Equations for Reflection from the Two Surfaces
Sum the InternalAmplitudes
Sum The SurfaceAmplitudes
The story behind this seems to be that particle theorist John Ellis and experimentalist Melissa Franklin were playing darts one evening at CERN in 1977, and a bet was made that would require Ellis to insert the word "penguin" somehow into his next research paper if he lost. He did lose, and was having a lot of trouble working out how he would do this. Finally, “the answer came to him when one evening,leaving CERN, he dropped by to visit some friends where he smoked an illegal substance”. While working on his paper later that night “in a moment of revelation he saw that the diagrams looked like penguins”.
Path integral gives us insight into the extremely nonlocal nature of quantum mechanics.
So, why not teach the path integral method
from the very beginning?
Path integral is much more difficult than
Schrodinger equation for simple NRQM
problems, viz., hydrogen atom and spin.
On the other hand, easier or comparable to the
canonical method for relativistic problems.
up and cause constructive interference! For the paths deviating from theclassical one, the change in the action (i.e. the phase) will be so large interms of h̄ that the interference will be destructive instead. It follows thatfor macroscopic particles only the classical trajectory will contribute to themotion.
cl
Paths interfere
constructively
Paths interfere
destructively
x
t
x
Figure 5.1: Emergence of the classical limit. There is constructive interferencebetween paths close to the classical trajectory (thick line) whereas the trajectoriesfurther away tend to cancel because of the rapidly changing sign of eiS[x(t)]/h̄.
For microscopic (quantum mechanical) particles on the other hand, theaction is typically of the order of h̄. Hence it takes a comparably large changein the action to achieve a significant change in the phase S[x(t)]/h̄. In otherwords, for very light particles even paths that deviate much from the classicalwill be of importance. In this case one can no longer talk about the trajectoryof the particle, but rather of a superposition of different paths.
In the limit h̄ → 0, even very small particles will obviously behave likeclassical particles, since their action will then become large compared to h̄.The limit h̄ → 0 is also the limit where the quantization of energy etc dis-appears, which is another effect of considering the classical limit of quantummechanics.
18
Visiting Einstein one day, I could not resist telling him about Feynman's
new way to express quantum theory. "Feynman has found a beautiful
picture to understand the probability amplitude for a dynamical system
to go from one specified configuration at one time to another specified
configuration at a later time. He treats on a footing of absolute equality
every conceivable history that leads from the initial state to the final
one, no matter how crazy the motion in between. The contributions of
these histories differ not at all in amplitude, only in phase. And the phase
is nothing but the classical action integral, apart from the Dirac factor h.
This prescription reproduces all of standard quantum theory. How could
one ever want a simpler way to see what quantum theory is all about!
Doesn't this marvelous discovery make you willing to accept the
quantum theory, Professor Einstein?"
Einstein replied in a serious voice, "I still cannot believe that God plays
dice. But maybe", he smiled, "I have earned the right to make my
mistakes."
John Wheeler
Up until now: H = Hmatter = KE + PE
Two more terms: Hradiation
Hinteraction
Htotal = Hmatter
+ Hradiation
+ Hinteraction
Fermi's First Golden Rule is the result of
applying second-order TDPT (time-dependent
perturbation theory) to quantum scattering
and resonances.
Fermi's Second Golden Rule is the result of
applying first-order TDPT (time-dependent
perturbation theory) to absorption.
Practicing the Golden Rule without a license is
a common offense, although it tends to pale
compared to the misuse of the uncertainty
relations.
Herbert Kroemer
"What Makes A Qualified Physicist?"
Quantum mechanics: Perturbation theory, first
and second order (Fermi's golden rules).
George Nickel
Why did Fermi refer to the second-order result as the First Rule? I would like to think that it was because Fermi considered scattering more important than absorption.
Electromagnetic interactions (photons)
Real Photons
Absorption
Stimulated Emission
Spontaneous Emission
Photo-ionization
Photon Scattering
Molecular Spectroscopy
Virtual Photons
Electrons in semiconductors
Phonon Scattering
Weak interaction (W and Z bosons)
beta decay
muon decay
tau decay
neutron decay
pion decay
Strong interaction (gluons)
alpha decay
Delta to proton+pion decay
proton-proton scattering
proton-neutron scattering
Requirements - I
2.) Single beta decay must be forbidden (m (A,Z) < m (A,Z+1))or at least strongly suppressed (large change in angular momentum)
1.) m(A,Z) > m(A,Z+2)
Na 23Na 23100 %100 %
Na22.98977
Na 24Na 2415.02h
Na 25Na 2560s
Na 26Na 261.07s
Na 27Na 270.29s
Na 28Na 2830.5ms
Na 29Na 2943ms43ms
Na 22Na 222.601y
Na 20Na 20446ms
Na 21Na 2122.5s
Na 19Na 1930ms?
Mg 24Mg 2478.99%
Mg 25Mg 2510.00%
Mg 26Mg 2611.01%
Mg 27Mg 279.45m
Mg 28Mg 2821.0h
Mg 29Mg 291.4s
Mg 30Mg 30~1.2s
Mg 20Mg 200.6s
Mg 21Mg 21122ms
Mg 22Mg 223.86s
Mg 23Mg 2311.3s
Al 23Al 230.47s
Al 24Al 242.07s
Al 25Al 257.23s
Al 26Al 267.3E5y
Al 27Al 27100%
Al 28Al 282.24m
Al 29Al 296.5m
Al 30Al 303.6s
Al 31Al 310.64s
Al26.9814
Mg24.305
Ne20.179
F18.998403
Ne 17Ne 17109ms
Ne 18Ne 181.67s
Ne 19Ne 1917.2s
Ne 20Ne 2090.51%
Ne 21Ne 210.27%
Ne 22Ne 229.22%
Ne 23Ne 2337.5s
Ne 24Ne 243.38m
Ne 25Ne 250.61s
F 17F 1764.5s
F 18F 18109.8m
F 19F 19100%
F 20F 2011.0s
F 21F 214.33s
F 22F 224.23s
F 23F 232.2s
O15.9994
N14.0067
O 13O 138.9ms
O 14O 1470.5s
O 15O 15122ms
O 16O 1699.758%
O 17O 170.038%
O 18O 180.204%
O 19O 1926.8s
O 20O 2013.5s
Neutrons
Pro
ton
s
Neu
tron
Exc
ess
Nuc
lides
Neu
tron
Exc
ess
Nuc
lides
min
usdec
ay
min
usdec
ayNeu
tron
Def
icie
ntN
uclid
es
Neu
tron
Def
icie
ntN
uclid
es
plu
sdec
ay
plu
sdec
ay
CHART OF THE NUCLIDESCHART OF THE NUCLIDES
C12.011
N 12N 1211.0ms
N 13N 139.97m
N 14N 1499.63%
N 15N 150.37%
N 16N 167.10s
N 17N 174.17s
N 18N 180.63s
N 19N 190.42s
C 9C 9127ms
C 10C 1019.3s
C 11C 1120.3m
C 12C 1298.89%
C 13C 131.11%
C 14C 145730y
C 15C 152.45s
C 16C 160.75s
B10.81
Be9.01218
B 8B 8770ms
B 10B 1020%
B 11B 1180%
B 12B 1220.4ms
B 13B 1317.3ms
B 14B 1416ms
Be 7Be 753.28d
Be 8Be 8~1E-16s
alpha~1E-16s
alpha
B 9B 9~8E-19sproton
~8E-19sproton
F 16F 16~1E-20sproton
~1E-20sproton
Be 6Be 6~5E-21sproton
~5E-21sproton
Be 9Be 9100%
Be 10Be 101.6E6y
Be 11Be 1113.8s
Be 12Be 12~11.4ms
Li6.941
He4.00260
H1.0079
~1E-21sproton
~1E-21sproton
Li 5Li 5 Li 6Li 67.5%
Li 7Li 792.5%
Li 8Li 8844ms
Li 9Li 9177ms
He 3He 30.00014%
He 4He 499.99986%
~8E-22sneutron~8E-22sneutron
He 5He 5 He 6He 6805ms
He 8He 8122ms
H 1H 199.985%
H 2H 20.015%
H 3H 312.33y
n 1n 110.4m
1
2
3
4
5
6
7
8
9
10
11
12
13
1 20
3 4 5 6
7 8
9 10
11 12
13 14
15 16
17 18
Branislav Streicher, Synthesis and spectroscopy of superheavy isotopes 3
Physical MotivationPredictions of the island of SHE • nuclei beyond Fm exist only
due to shell effects
• predictions of highly stabilized SHE (Ttheo ~ min -y)
• failure to synthesize SHE by reactions of the type Pb + Pb (U + U)
1) Production of SHE via “hot” and “cold” fusion2) Systematic study of nuclear structure of transfermium isotopes
SHE location – openedZ = 114, 120, 126
N = 172, 184
fundamentals of spin-orbitforce
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