1. Total Angular Momentum
Orbital angular momentum
Spin angular momentum
Total angular momentum
L, Lz, S, SzJ and Jz are quantized

2. Total Angular Momentum
If j and mj are quantum numbers for the single electron (hydrogen atom)
Quantization of the magnitudes
The total angular momentum quantum number for the single electron can only have the values

3. The Total Angular Momentum Diagram
Figure 8.5 When forming the total angular momentum from the orbital and spin angular momenta, the addition must be done vectorially,

4. Spin-Orbit Coupling The dipole potential energy
An effect of the spins of the electron and the orbital angular momentum interaction is called spin-orbit coupling.
is th·e magnetic field due to the proton
where cos a is the angle between
The dipole potential energy
The spin magnetic moment µ .

5. Total Angular Momentum
No external magnetic field: J can have a fixed valuein only one direction. This direction can be chosen randomly
Only Jz can be known because the uncertainty principle forbids Jx or Jy from being known at the same time as Jz

6. Total Angular Momentum
With an external magnetic field:
will precess about

7. Total Angular Momentum
Now the selection rules for a single-electron atom become
Δn = anything Δℓ = ±1
Δmj = 0, ±1 Δj = 0, ±1
Hydrogen energy-level diagram for n = 2 and n = 3 with the spin-orbit splitting

8. The Energy-Level Diagram of Sodium
Fine structure splitting is too small on this scale(not shown)

9. Many-Electron Atoms Hund’s rules:
The total spin angular momentum S should be maximized to the extent possible without violating the Pauli exclusion principle.
Insofar as rule 1 is not violated, L should also be maximized.
For atoms having subshells less than half full, J should be minimized.
We label with 1 and 2 the two-electron atom
There are LS coupling and jj coupling to combine four angular momenta J.

10. LS Coupling
This is used for most atoms when the magnetic field is weak.
If two electrons are in a single subshell, S = 0 or 1 depending on whether the spins are antiparallel or parallel.
For given L, there are 2S + 1 values of J
For L > S, J goes from L − S to L + S
For L < S, there are fewer than 2S + 1 possible J values
The value of 2S + 1 is the multiplicity of the state

11. Table 8-2 p287

12. LS Coupling The notation for a single-electron atom becomes n2S+1 LJ
The letters and numbers are called spectroscopic symbols.
There are singlet states (S = 0) and triplet states (S = 1) for two electrons.

13. LS Coupling Magnesium(0ne electron in 3s subshell and the other excited to the nl subshell)
There are separated energy levels according to whether they are S = 0 or 1
Allowed transitions must have ΔS = 0
No allowed (forbidden) transitions are possible between singlet and triplet states with much lower probability

14. LS Coupling The allowed transitions for the LS coupling scheme are
ΔJ = 0, ±1 (J = 0 → J = 0 is forbidden)
A magnesium atom excited to the 3s3p triplet state has no lower triplet state to which it can decay.
It is called metastable, because it lives for such a long time on the atomic scale.

15. jj Coupling
It is for the heavier elements, where the nuclear charge causes the spin-orbit interactions to be as strong as the force between the individual and .

16. Mercury

17. Figure 8.11 (a) Two electrons having orbital angular momentum quantum numbers of 1 and 2 combine to form L values of 1, 2, 3. (b) Two electrons having spin angular quantum numbers of 1/2 and 1/2 form S values of 0 and 1.
Figure 8-11 p290

18. Figure 8. 12 S and L are antialigned and form J = L + S
Figure 8.12 S and L are antialigned and form J = L + S. Both S and L precess about J, while J precesses about the z axis.
Figure 8-12 p290

20. Clicker - Questions

21. 8.3: Anomalous Zeeman Effect
More than three closely spaced optical lines were observed.
The interaction that splits the energy levels in an external magnetic field is caused by interaction.
The magnetic moment depends on
The 2J + 1 degeneracy for a given total angular momentum state J is removed by the effect of the
If the is small compared to internal magnetic field, then and precess about while precesses slowly about
Orbital contribution
and
Spin magnetic moment

22. Total Angular Momentum
With an external magnetic field:
will precess about

23. Anomalous Zeeman Effect
The total magnetic moment is
The magnetic total angular momentum numbers mJ from −J to J in integral steps.
splits each state J into 2J + 1 equally spaced levels separated ΔE = V.
For photon transitions between energy levels
ΔmJ = ±1, 0 but is forbidden when ΔJ = 0.
μB is the Bohr magneton and
it is called the Landé g factor

24. Figure 8.15 Examples of transitions for the normal Zeeman effect. The nine possible transitions are labeled, but there are only three distinctly different energies because the split energy levels are equally spaced (∆E) for both the 1D2 and 1P1 states.
Figure 8.15 Examples of transitions for the normal Zeeman effect. The nine possible transitions are labeled, but there are only three distinctly different energies because the split energy levels are equally spaced (∆E) for both the 1D2 and 1P1 states
Figure 8-15 p293

25. Anomalous Zeeman effect for Na
Figure 8.16 Schematic diagram of anomalous Zeeman effect for sodium (energy levels not to scale). With Bext = 0 for the unperturbed states, there is only one transition. With the spin-orbit interaction splitting the 2P state into two states, there are two possible transitions when Bext = 0. Finally, Bext splits J into 2J + 1 components, each with a different mJ. The energy splitting ∆E for each major state is different because ΔE = gmJ (eh2m)Bext and the Landé g factor for g[∆E(2S1/2)] > g[∆E(2P3/2)] > g[∆E(2P1/2)]. All allowed transitions are shown.
Figure 8-16 p294

26. Rydberg Atom
An atom that is highly excited with the outermost electron in a high energy level near ionization
Properties of Rydberg atoms:

27. Useful Combinations of Constants

28. Solution: In the first excited state, go to the next higher level
Solution: In the first excited state, go to the next higher level. In neon one of the 2p electrons is promoted to 3s, so the configuration is 2p^5 3s^1 . By the same reasoning the first excited state of xenon is 5p^5 6s^1.

29. The 3s state of Na has energy of -5. 14eV
The 3s state of Na has energy of -5.14eV.Determine the effective nuclear charge.
From Figure 8.4 we see that the radius of Na is about 0.16 nm. We know that for single-electron atoms it holds

30. Problem 8.21

31. Problem 8.31

32. Problem 8.33

33. Problem 8.15

34. Problem 8.17

35. Problem 8.19

36. Problem

37. Problem 10.19

38. Problem 10.20

39. Problem 10.22

40. Why does Bose-Einstein Condensation of Atoms Occur?
Rb atom Eric Cornell and Carl Wieman
Na atom Wolfgang Ketterle______
Nobel Price 2001
Consider boson and fermion wave functions of two identical particles labeled “1” and “2”. For now they can be either fermions or bosons:
Solutions:
Identical probability density the same. The solutions to this equation are
+ symmetric =boson antisymmetric=fermion
Proof:
= nonzero probability occupying the same state favors to be in the lower states for Bose-Einstein Condensation
Two bosons can occupy the same state this can be generalized to many bosons and under favorable conditions Bose- Einstein condensation occurs. Bosons have integer spins and Fermions half integer spins.

41. Bose –Einstein condensation in Gases

43. Clicker - Questions

44. Stimulated Emission and Lasers
Tunable laser:
The emitted radiation wavelength can be adjusted as wide as 200 nm.
Semi conductor lasers are replacing dye lasers.
Free-electron laser:
Place the “Free-electron laser” and diagram on the next slide.

45. From: Demonstration of electron acceleration in a laser-driven dielectric microstructure (Byer et al.Vol 503,nature,2013) a b
DLA structure and experimental set-up. a, Scanning electron microscope image of the longitudinal cross-section of a DLA structure fabricated as depicted in Extended Data Fig. 1a. Scale bar, 2 mm.b, Experimental set-up. Inset, a diagram of the DLA structure indicating the field polarization direction and the effective periodic phase reset, depicted as alternating red (acceleration) and black (deceleration) arrows. A snapshot of the simulated fields in the structure shows the corresponding spatial modulation in the vacuum channel.

47. Stimulated Emission and Lasers
This laser relies on charged particles.
A series of magnets called wigglers is used to accelerate a beam of electrons.
Free electrons are not tied to atoms; they aren’t dependent upon atomic energy levels and can be tuned to wavelengths well into the UV part of the spectrum.
Add previous slides diagram on this slide.

48. Scientific Applications of Lasers
An extremely coherent and nondivergent beam is used in making precise determination of large and small distances. The speed of light in a vacuum is defined. c = 299,792,458 m/s.
Pulsed lasers are used in thin-film deposition to study the electronic properties of different materials.
The use of lasers in fusion research
Inertial confinement:
A pellet of deuterium and tritium would be induced into fusion by an intense burst of laser light coming simultaneously from many directions.

49. Holography Consider laser light emitted by a reference source R.
The light through a combination of mirrors and lenses can be made to strike both a photographic plate and an object O.
The laser light is coherent; the image on the film will be an interference pattern.

50. Holography
After exposure this interference pattern is a hologram, and when the hologram is illuminated from the other side, a real image of O is formed.
If the lenses and mirrors are properly situated, light from virtually every part of the object will strike every part of the film.
Each portion of the film contains enough information to reproduce the whole object!

51. Holography Transmission hologram:
The reference beam is on the same side of the film as the object and the illuminating beam is on the opposite side.
Reflection hologram:
Reverse the positions of the reference and illuminating beam.
The result will be a white light hologram in which the different colors contained in white light provide the colors seen in the image.
Interferometry:
Two holograms of the same object produced at different times can be used to detect motion or growth that could not otherwise be seen.

52. Quantum Entanglement, Teleportation, and Information
Schrödinger used the term “quantum entanglement” to describe a strange correlation between two quantum systems. He considered entanglement for quantum states acting across large distances, which Einstein referred to as “spooky action at a distance.”
Quantum teleportation:
No information can be transmitted through only quantum entanglement, but transmitting information using entangled systems in conjunction with classical information is possible.

53. Quantum Entanglement, Teleportation, and Information
Alice, who does not know the property of the photon, is spacially
separated from Bob and tries to transfer information about photons.
A beam splitter can be used to produce two additional photons that can be used to trigger a detector.
Alice can manipulate her quantum system and send that information over a classical information channel to Bob.
Bob then arranges his part of the quantum system to detect information.

54. Other Laser Applications
Used in surgery to make precise incisions
Ex: eye operations
We see in everyday life such as the scanning devices used by supermarkets and other retailers
Ex. Bar code of packaged product
CD and DVD players
Laser light is directed toward disk tracks that contain encoded information.
The reflected light is then sampled and turned into electronic signals that produce a digital output.