1. Clicker Questions Lecture Slides Professor John Price, Spring 2019
Physics 2130 Foundations of Modern Physics Quantum Mechanics Part IV: Applications
Clicker Questions
Lecture Slides
Professor John Price, Spring 2019

2. Applications of Quantum Mechanics
Multi-electron atoms and the periodic table (TZD Ch. 10)
Metals, insulators, semiconductors (TZD , 14.2)
Nuclear spin, NMR, MRI (TZD 16.1,16.2,9.3,9.4,9.5,9.8)
Quantum Computing
J. Preskill:
A. Helwer on Youtube:
Clicker
a. start / stop
b, hide/ unhide
c. ppt-1page fwd
d. ppt 1 pg back
e. select correct answer

3. 1≤ 𝑍 𝑒𝑓𝑓 ≤𝑍 Screened Coulomb Potential
. Discuss the form of the v transformation formula
. Why plus not minus
. Discuss that is always smaller than c
1≤ 𝑍 𝑒𝑓𝑓 ≤𝑍

4. Hydrogen radial probability distributions
. Discuss the form of the v transformation formula
. Why plus not minus
. Discuss that is always smaller than c

5. +Ze -e What is 𝑍 𝑒𝑓𝑓 for the outermost electron? nucleus+1
- 1 +Z
-(Z-1)
other electrons
+Ze
electron being solved for
. Discuss the form of the v transformation formula
. Why plus not minus
. Discuss that is always smaller than c -e
Clicker Slide 120 Physics 2130, Spring 2019

6. +Ze -e What is 𝑍 𝑒𝑓𝑓 for the innermost electron? nucleus+1
- 1 +Z
-(Z-1)
other electrons
+Ze -e
. Discuss the form of the v transformation formula
. Why plus not minus
. Discuss that is always smaller than c
electron being solved for
Clicker Slide 121 Physics 2130, Spring 2019

7. What is 𝑍 𝑒𝑓𝑓 ? +Ze -e 1≤ 𝑍 𝑒𝑓𝑓 ≤2 nucleus other electrons
We are often interested in
valence electrons, so -e
1≤ 𝑍 𝑒𝑓𝑓 ≤2
. Discuss the form of the v transformation formula
. Why plus not minus
. Discuss that is always smaller than c
electron being solved for

8. . Discuss the form of the v transformation formula
. Why plus not minus
. Discuss that is always smaller than c

9. . Discuss the form of the v transformation formula
. Why plus not minus
. Discuss that is always smaller than c

10. What is the electronic configuration of nitrogen?
1s22s1
1s22s2
1s22s22p1
1s22s22p2
1s22s22p3
. Discuss the form of the v transformation formula
. Why plus not minus
. Discuss that is always smaller than c
Clicker Slide 122 Physics 2130, Spring 2019

11. . Discuss the form of the v transformation formula
. Why plus not minus
. Discuss that is always smaller than c

12. Estimate 𝑍𝑒𝑓𝑓 for helium:
1.0
1.4
2.0
2.4
. Discuss the form of the v transformation formula
. Why plus not minus
. Discuss that is always smaller than c
Clicker Slide 123 Physics 2130, Spring 2019

13. . Discuss the form of the v transformation formula
. Why plus not minus
. Discuss that is always smaller than c

14. 2p states (n=2, l=1) m=0 m=±1 states
. Discuss the form of the v transformation formula
. Why plus not minus
. Discuss that is always smaller than c
m=0
m=±1 states

15. Crystals CaSO4 2H2O Blue: Ca Red: Oxygen Yellow: Sulfer
. Discuss the form of the v transformation formula
. Why plus not minus
. Discuss that is always smaller than c
CaSO4 2H2O
Blue: Ca
Red: Oxygen
Yellow: Sulfer
Pink: Oxygen in H2O
Selenite crystals, Niaca Mine, Chihuahua

16. Crystals
. Discuss the form of the v transformation formula
. Why plus not minus
. Discuss that is always smaller than c
Bravais lattice: An elementary repeating pattern that can fill all of space. Every point has exactly the same environment.
Crystal: A Bravais lattice plus a set or “basis” of atoms associated with every lattice point. In this case, on Na+ and on Cl-.

17. X-ray diffraction Agilent Supernova XRD
. Discuss the form of the v transformation formula
. Why plus not minus
. Discuss that is always smaller than c
Agilent Supernova XRD
Sources: Dual Cu/Mo X-ray sources for protein and small molecule work. Quick and easy switching between sources.
135mm Atlas CCD detector on extended two-theta arm.
Oxford Instruments Cryojet HT: Provides liquid nitrogen cooling, giving a temperature range of K.

18. Glasses SiO2 quartz crystal quartz glass or fused silica
. Discuss the form of the v transformation formula
. Why plus not minus
. Discuss that is always smaller than c
quartz crystal
quartz glass or fused silica

19. Two-particle correlation functions
. Discuss the form of the v transformation formula
. Why plus not minus
. Discuss that is always smaller than c
Probability to find an atom or molecule a distance r from another molecule

20. Bonding in solids . Discuss the form of the v transformation formula
. Why plus not minus
. Discuss that is always smaller than c

21. Fermi surface of copperkz ky kx
. Discuss the form of the v transformation formula
. Why plus not minus
. Discuss that is always smaller than c

22. Electron “normal” Zeeman effect (orbital angular momentum)
𝐵 =0
𝐵 = 𝐵 𝑧 𝑧
l=1
l=0
. Discuss the form of the v transformation formula
. Why plus not minus
. Discuss that is always smaller than c
A B C D E
Clicker Slide 124 Physics 2130, Fall 2019

23. Electron “normal” Zeeman effect (orbital angular momentum) What is δf?
𝐵 =0
𝐵 = 𝐵 𝑧 𝑧
m=1
δf=δE/h
14 GHz/T
12 MHz/T
28 GHz/T
42 MHz/T
18 kHz/T
l=1
m=0
m=-1
l=0
. Discuss the form of the v transformation formula
. Why plus not minus
. Discuss that is always smaller than c
Clicker Slide 125 Physics 2130, Fall 2019

24. Electron “anomalous” Zeeman effect (spin angular momentum) What is δf?
𝐵 =0
𝐵 = 𝐵 𝑧 𝑧
ms=+1/2
14 GHz/T
12 MHz/T
28 GHz/T
42 MHz/T
18 kHz/T
s=1/2
δf=δE/h
ms=-1/2
. Discuss the form of the v transformation formula
. Why plus not minus
. Discuss that is always smaller than c
Clicker Slide 126 Physics 2130, Fall 2019

25. Proton NMR (spin angular momentum) What is δf? 𝐵 =0 𝐵 = 𝐵 𝑧 𝑧
𝐵 = 𝐵 𝑧 𝑧
ms=-1/2
14 GHz/T
12 MHz/T
28 GHz/T
42 MHz/T
18 kHz/T
s=1/2
δf=δE/h
ms=+1/2
. Discuss the form of the v transformation formula
. Why plus not minus
. Discuss that is always smaller than c
Clicker Slide 127 Physics 2130, Fall 2019

26. What system corresponds to each sketch?
continuum
E=0
A B C D E F
What system corresponds to each sketch?
Some options: harmonic oscillator, free particle, hydrogen, spin-1/2 particle in a magnetic field, infinite square well, finite square well
Every system must have a ground state.
. Discuss the form of the v transformation formula
. Why plus not minus
. Discuss that is always smaller than c

27. NMR Today NO Spatial Resolution? YES YES Frequency Resolution? NO
TD NMR, oil content in seed crops
Functional MRI of the human brain
YES Frequency Resolution? NO
Especially 1H, 13C, 15N, 31P
Structure of bio-molecules by multi-dimension multi-nuclear NMR spectroscopy
MRI spectroscopy of the human brain 27

28. Energies for proton NMR
100
1015
105
1010
covalent
electrostatic
chemical bonds
hydrogen
VdW
45 MHz 1 GHz
300K
proton Larmor freq.
magnetic dipole-dipole
Especially 1H, 13C, 15N, 31P
chemical shifts
J couplings
Frequency (Hz) 28

29. Liquid-phase proton FT-NMR spectroscopy
Coil
Transmit
To make an NMR signal you put a coil of wire near the aligned protons.
*click*
By sending a brief radio-frequency pulse into the coil to can create a varying magnetic field that has the effect of tipping the protons over so they are now perpendicular to the magnetic field. This is called a 90-degree pulse and this part of NMR is called the transmit phase. The magnetic field will try to realign the proton...
Transition to the next slide is required here to make the GIF animations start at the right moment. Do not separate these two slides.

30. Liquid-phase proton FT-NMR spectroscopy
frequency
NMR Spectrum
Coil
…but because the proton has spin, like a gyroscope, it will precess around the magnetic field direction before it realigns. The precession creates a time varying magnetic field through the coil, and this induces a voltage according to Faraday's law. The induced signal is called a free induction decay, or FID, and this is the receive phase of pulsed NMR. Its called FID because it is a free motion of the proton that induces a signal and quickly decays away.
*click*
The precession frequency depends on the strength of the magnetic field. Gen3MR designs will have precession (or Larmor) frequencies of 15 to 20 MHz. Higher frequencies give stronger signals but require larger and more expensive magnets.
We have already said that the proton will realign after T1 and that time is shown about right in this animation, but of course the precession rate has been drastically slowed down so you can see the motion. From this animation you might think that the FID signal would last a time T1, but that is not the case. There are really many many protons and they are not all in exactly the same magnetic field, so they dont precess at exactly the same rate. They get out of phase and the signal disappears after a time T2, which is about 100 microseconds for our technology.
Receive

31. Demo: acetone-free nail polish remover
Our mission is…
We call our technology Gen3MR because it represents a third generation of magnetic resonance technology.
Our instruments will provide fow measurement, flow control, and analytical measurements that cannot be provided by any technology on the market today.
Here is a concept of an instrument that would both measure flow rate and the solids fraction of the fluid. It could be applied for monitoring a polishing slurry.
We will go into more detail below but the key advantages of our technology are….
ratio of ethanol/ethyl acetate/water in nail polish remover 31

32. NMR = nuclear magnetic resonance
1) The original Edison tin-foil cylinder recorder. 2) The first disk recorder. 3) Jan Kubelik circa An acousto/mechanical recording session

33. NMR Spectrometers Today
Bruker 400 MHz AVANCE III
Varian 900 MHz (¼ Scale)
Our instruments represent a radical departure from existing NMR devices.
NMR was discovered in Applications to chemical analysis were recognized very early and by 1956 Varian Corp was selling a 40 MHz continuous wave instrument for lab use. Laboratory instruments with chemical applications have continued to evolve. They are large, costly and require specially trained staff. We call these generation 1 instruments.
NMR is also used today in many industrial setting for process analysis, development and for quality control. We call these generation 2 instruments. They arey also large and require specialist staff.
Anasazi Aii 60 MHz
Qualion 60 MHz Refinery Analyzer

34. New Table-top NMR Spectrometers (approx. to scale)
80 MHz (2013)
45 MHz (2010) 8”
picoSpin/Thermo Fisher
Nanalysis 60 MHz (2012)
Magritek 42 MHz (2012)
Oxford 60 MHz (2013)
Bruker 60 MHz (2013)

35. Slide by Joe Lykken, Fermilab
Our instruments represent a radical departure from existing NMR devices.
NMR was discovered in Applications to chemical analysis were recognized very early and by 1956 Varian Corp was selling a 40 MHz continuous wave instrument for lab use. Laboratory instruments with chemical applications have continued to evolve. They are large, costly and require specially trained staff. We call these generation 1 instruments.
NMR is also used today in many industrial setting for process analysis, development and for quality control. We call these generation 2 instruments. They arey also large and require specialist staff. 35

36. Physical qubit technologies (slides by Tanisha Bassan)
Our instruments represent a radical departure from existing NMR devices.
NMR was discovered in Applications to chemical analysis were recognized very early and by 1956 Varian Corp was selling a 40 MHz continuous wave instrument for lab use. Laboratory instruments with chemical applications have continued to evolve. They are large, costly and require specially trained staff. We call these generation 1 instruments.
NMR is also used today in many industrial setting for process analysis, development and for quality control. We call these generation 2 instruments. They arey also large and require specialist staff. 36

37. Physical qubit technologies (slides by Tanisha Bassan)
Our instruments represent a radical departure from existing NMR devices.
NMR was discovered in Applications to chemical analysis were recognized very early and by 1956 Varian Corp was selling a 40 MHz continuous wave instrument for lab use. Laboratory instruments with chemical applications have continued to evolve. They are large, costly and require specially trained staff. We call these generation 1 instruments.
NMR is also used today in many industrial setting for process analysis, development and for quality control. We call these generation 2 instruments. They arey also large and require specialist staff. 37

38. Physical qubit technologies (slides by Tanisha Bassan)
Our instruments represent a radical departure from existing NMR devices.
NMR was discovered in Applications to chemical analysis were recognized very early and by 1956 Varian Corp was selling a 40 MHz continuous wave instrument for lab use. Laboratory instruments with chemical applications have continued to evolve. They are large, costly and require specially trained staff. We call these generation 1 instruments.
NMR is also used today in many industrial setting for process analysis, development and for quality control. We call these generation 2 instruments. They arey also large and require specialist staff. 38

39. Transmon qubit (figures by Christian Dickel)
“transmission line shunted plasma oscillation qubit”
Our instruments represent a radical departure from existing NMR devices.
NMR was discovered in Applications to chemical analysis were recognized very early and by 1956 Varian Corp was selling a 40 MHz continuous wave instrument for lab use. Laboratory instruments with chemical applications have continued to evolve. They are large, costly and require specially trained staff. We call these generation 1 instruments.
NMR is also used today in many industrial setting for process analysis, development and for quality control. We call these generation 2 instruments. They arey also large and require specialist staff. 39

40. Transmon qubit (figures by Christian Dickel)
Our instruments represent a radical departure from existing NMR devices.
NMR was discovered in Applications to chemical analysis were recognized very early and by 1956 Varian Corp was selling a 40 MHz continuous wave instrument for lab use. Laboratory instruments with chemical applications have continued to evolve. They are large, costly and require specially trained staff. We call these generation 1 instruments.
NMR is also used today in many industrial setting for process analysis, development and for quality control. We call these generation 2 instruments. They arey also large and require specialist staff. 40

41. Transmon qubit (figures by Christian Dickel)
Our instruments represent a radical departure from existing NMR devices.
NMR was discovered in Applications to chemical analysis were recognized very early and by 1956 Varian Corp was selling a 40 MHz continuous wave instrument for lab use. Laboratory instruments with chemical applications have continued to evolve. They are large, costly and require specially trained staff. We call these generation 1 instruments.
NMR is also used today in many industrial setting for process analysis, development and for quality control. We call these generation 2 instruments. They arey also large and require specialist staff. 41

42. Amit Vainsencher with Google’s 72-qubit quantum processor
Our instruments represent a radical departure from existing NMR devices.
NMR was discovered in Applications to chemical analysis were recognized very early and by 1956 Varian Corp was selling a 40 MHz continuous wave instrument for lab use. Laboratory instruments with chemical applications have continued to evolve. They are large, costly and require specially trained staff. We call these generation 1 instruments.
NMR is also used today in many industrial setting for process analysis, development and for quality control. We call these generation 2 instruments. They arey also large and require specialist staff. 42