- 1.1. Different views of the same experiment.
- 1.2. Coordinate systems for the Lorentz transformation.
- 1.3. Example elastic collision seen by different observers.
- 1.4. A completely inelastic collision.
- 2.1. The classical picture of a vector.
- 2.2. Spike diagram of a vector.
- 2.3. More dimensions.
- 2.4. Infinite dimensions.
- 2.5. The classical picture of a function.
- 2.6. Forming the dot product of two vectors.
- 2.7. Forming the inner product of two functions.
- 2.8. Illustration of the eigenfunction concept.
- 3.1. The old incorrect Newtonian physics.
- 3.2. The correct quantum physics.
- 3.3. Illustration of the Heisenberg uncertainty principle.
- 3.4. Classical picture of a particle in a closed pipe.
- 3.5. Quantum mechanics picture of a particle in a closed pipe.
- 3.6. Definitions for one-dimensional motion in a pipe.
- 3.7. One-dimensional energy spectrum for a particle in a pipe.
- 3.8. One-dimensional ground state of a particle in a pipe.
- 3.9. Second and third lowest one-dimensional energy states.
- 3.10. Definition of all variables for motion in a pipe.
- 3.11. True ground state of a particle in a pipe.
- 3.12. True second and third lowest energy states.
- 3.13. A combination of and seen at some typical times.
- 4.1. Classical picture of an harmonic oscillator.
- 4.2. The energy spectrum of the harmonic oscillator.
- 4.3. Ground state of the harmonic oscillator
- 4.4. Wave functions and .
- 4.5. Energy eigenfunction .
- 4.6. Arbitrary wave function (not an energy eigenfunction).
- 4.7. Spherical coordinates of an arbitrary point P.
- 4.8. Spectrum of the hydrogen atom.
- 4.9. Ground state wave function of the hydrogen atom.
- 4.10. Eigenfunction .
- 4.11. Eigenfunction , or 2p.
- 4.12. Eigenfunction (and ).
- 4.13. Eigenfunctions 2p, left, and 2p, right.
- 4.14. Hydrogen atom plus free proton far apart.
- 4.15. Hydrogen atom plus free proton closer together.
- 4.16. The electron being anti-symmetrically shared.
- 4.17. The electron being symmetrically shared.
- 5.1. State with two neutral atoms.
- 5.2. Symmetric sharing of the electrons.
- 5.3. Antisymmetric sharing of the electrons.
- 5.4. Approximate solutions for the hydrogen (left) and helium (right) atoms.
- 5.5. Abbreviated periodic table of the elements.
- 5.6. Approximate solutions for lithium (left) and beryllium (right).
- 5.7. Example approximate solution for boron.
- 5.8. Periodic table of the elements.
- 5.9. Covalent sigma bond consisting of two 2p states.
- 5.10. Covalent pi bond consisting of two 2p states.
- 5.11. Covalent sigma bond consisting of a 2p and a 1s state.
- 5.12. Shape of an sp hybrid state.
- 5.13. Shapes of the sp and sp hybrids.
- 6.1. Allowed wave number vectors, left, and energy spectrum, right.
- 6.2. Ground state of a system of noninteracting bosons in a box.
- 6.3. The system of bosons at a very low temperature.
- 6.4. The system of bosons at a relatively low temperature.
- 6.5. Ground state system energy eigenfunction for a simple model system.
- 6.6. State with 5 times the single-particle ground state energy.
- 6.7. Distinguishable particles: 9 energy eigenfunctions for distribution A.
- 6.8. Distinguishable particles: 12 energy eigenfunctions for distribution B.
- 6.9. Bosons: only 3 energy eigenfunctions for distribution A.
- 6.10. Bosons: also only 3 energy eigenfunctions for distribution B.
- 6.11. Ground state of noninteracting electrons (fermions) in a box.
- 6.12. Severe confinement in the -direction.
- 6.13. Severe confinement in both the and directions.
- 6.14. Severe confinement in all three directions.
- 6.15. A system of fermions at a nonzero temperature.
- 6.16. Particles at high-enough temperature and low-enough particle density.
- 6.17. Ground state of noninteracting electrons (fermions) in a periodic box.
- 6.18. Conduction in the free-electron gas model.
- 6.19. Sketch of electron energy spectra in solids at absolute zero temperature.
- 6.20. Sketch of electron energy spectra in solids at a nonzero temperature.
- 6.21. Potential energy seen by an electron along a line of nuclei.
- 6.22. Potential energy in the one-dimensional Kronig & Penney model.
- 6.23. Example Kronig & Penney spectra.
- 6.24. Spectrum against wave number in the extended zone scheme.
- 6.25. Spectrum against wave number in the reduced zone scheme.
- 6.26. Some one-dimensional energy bands for a few basic semiconductors.
- 6.27. Spectrum against wave number in the periodic zone scheme.
- 6.28. Schematic of the zinc blende (ZnS) crystal.
- 6.29. First Brillouin zone of the FCC crystal.
- 6.30. Sketch of a more complete spectrum of germanium.
- 6.31. Vicinity of the band gap of intrinsic and doped semiconductors.
- 6.32. Relationship between conduction electron density and hole density.
- 6.33. The p-n junction in thermal equilibrium.
- 6.34. Schematic of the operation of an p-n junction.
- 6.35. Schematic of the operation of an n-p-n transistor.
- 6.36. Vicinity of the band gap in the electron energy spectrum of an insulator.
- 6.37. Peltier cooling.
- 6.38. An example Seebeck voltage generator.
- 6.39. The Galvani potential does not produce a usable voltage.
- 6.40. The Seebeck effect is not directly measurable.
- 7.1. The ground state wave function looks the same at all times.
- 7.2. The first excited state at all times.
- 7.3. Concept sketch of the emission of an electromagnetic photon by an atom.
- 7.4. Addition of angular momenta in classical physics.
- 7.5. Longest and shortest possible final momenta in classical physics.
- 7.6. A combination of two energy eigenfunctions seen at some typical times.
- 7.7. Energy slop diagram.
- 7.8. Schematized energy slop diagram.
- 7.9. Emission and absorption of radiation by an atom.
- 7.10. Dirac delta function.
- 7.11. The real part (red) and envelope (black) of an example wave.
- 7.12. The wave moves with the phase speed.
- 7.13. The real part and magnitude or envelope of a wave packet.
- 7.14. The velocities of wave and envelope are not equal.
- 7.15. A particle in free space.
- 7.16. An accelerating particle.
- 7.17. A decelerating particle.
- 7.18. Unsteady solution for the harmonic oscillator.
- 7.19. A partial reflection.
- 7.20. An tunneling particle.
- 7.21. Penetration of an infinitely high potential energy barrier.
- 7.22. Schematic of a scattering wave packet.
- 8.1. Separating the hydrogen ion.
- 8.2. The Bohm experiment before the Venus measurement (left), and immediately after it (right).
- 8.3. Spin measurement directions.
- 8.4. Earth's view of events and that of a moving observer.
- 8.5. The space-time diagram of Wheeler's single electron.
- 8.6. Bohm's version of the Einstein, Podolski, Rosen Paradox.
- 8.7. Nonentangled positron and electron spins; up and down.
- 8.8. Nonentangled positron and electron spins; down and up.
- 8.9. The wave functions of two universes combined
- 8.10. The Bohm experiment repeated.
- 8.11. Repeated experiments on the same electron.
- 10.1. Billiard-ball model of the salt molecule.
- 10.2. Billiard-ball model of a salt crystal.
- 10.3. The salt crystal disassembled to show its structure.
- 10.4. The lithium atom, scaled more correctly than before.
- 10.5. Body-centered-cubic (BCC) structure of lithium.
- 10.6. Fully periodic wave function of a two-atom lithium ``crystal.''
- 10.7. Flip-flop wave function of a two-atom lithium ``crystal.''
- 10.8. Wave functions of a four-atom lithium ``crystal.''
- 10.9. Reciprocal lattice of a one-dimensional crystal.
- 10.10. Schematic of energy bands.
- 10.11. Schematic of merging bands.
- 10.12. A primitive cell and primitive translation vectors of lithium.
- 10.13. Wigner-Seitz cell of the BCC lattice.
- 10.14. Schematic of crossing bands.
- 10.15. Ball and stick schematic of the diamond crystal.
- 10.16. Assumed simple cubic reciprocal lattice in cross-section.
- 10.17. Occupied states for one, two, and three electrons per lattice cell.
- 10.18. Redefinition of the occupied wave number vectors into Brillouin zones.
- 10.19. Second, third, and fourth zones in the periodic zone scheme.
- 10.20. The wavenumber vector of a sample free electron wave function.
- 10.21. The grid of nonzero Hamiltonian perturbation coefficients.
- 10.22. Tearing apart of the wave number space energies.
- 10.23. Effect of a lattice potential on the energy.
- 10.24. Bragg planes seen in wave number space cross section.
- 10.25. Occupied states if there are two valence electrons per lattice cell.
- 10.26. Smaller lattice potential.
- 10.27. Depiction of an electromagnetic ray.
- 10.28. Law of reflection in elastic scattering from a plane.
- 10.29. Scattering from multiple ``planes of atoms.''
- 10.30. Difference in travel distance when scattered from P rather than O.
- 11.1. An arbitrary system eigenfunction for 36 distinguishable particles.
- 11.2. An arbitrary system eigenfunction for 36 identical bosons.
- 11.3. An arbitrary system eigenfunction for 33 identical fermions.
- 11.4. Illustrative small model system having 4 distinguishable particles.
- 11.5. The number of system energy eigenfunctions for a simple model system.
- 11.6. Number of energy eigenfunctions on the oblique energy line.
- 11.7. Probabilities if there is uncertainty in energy.
- 11.8. Probabilities if shelf 1 is a nondegenerate ground state.
- 11.9. Like the previous figure, but at a lower temperature.
- 11.10. Like the previous figures, but at a still lower temperature.
- 11.11. Schematic of the Carnot refrigeration cycle.
- 11.12. Schematic of the Carnot heat engine.
- 11.13. A generic heat pump next to a reversed Carnot one.
- 11.14. Comparison of two different integration paths for finding the entropy.
- 11.15. Specific heat at constant volume of gases.
- 11.16. Specific heat at constant pressure of solids.
- 12.1. Example bosonic ladders.
- 12.2. Example fermionic ladders.
- 12.3. Triplet and singlet states in terms of ladders
- 12.4. Clebsch-Gordan coefficients of two spin one half particles.
- 12.5. Clebsch-Gordan coefficients for second angular momentum one-half.
- 12.6. Clebsch-Gordan coefficients for second angular momentum one.
- 13.1. Relationship of Maxwell's first equation to Coulomb's law.
- 13.2. Maxwell's first equation for a more arbitrary region.
- 13.3. The net number of outgoing field lines is a measure for the net charge.
- 13.4. The net number of magnetic field lines leaving a region is always zero.
- 13.5. Electric power generation.
- 13.6. Two ways to generate a magnetic field.
- 13.7. Electric field and potential of a uniform spherical charge.
- 13.8. Electric field of a two-dimensional line charge.
- 13.9. Field lines of a vertical electric dipole.
- 13.10. Electric field of a two-dimensional dipole.
- 13.11. Field of an ideal magnetic dipole.
- 13.12. Electric field of an almost ideal two-dimensional dipole.
- 13.13. Magnetic field lines around an infinite straight electric wire.
- 13.14. An electromagnet consisting of a single wire loop.
- 13.15. A current dipole.
- 13.16. Electric motor using a single wire loop.
- 13.17. Computation of the moment on a wire loop in a magnetic field.
- 13.18. Larmor precession of the expectation spin.
- 13.19. Probability of being able to find the nuclei at elevated energy.
- 13.20. Maximum probability of finding the nuclei at elevated energy.
- 13.21. Effect of a perturbing magnetic field rotating at the Larmor frequency.
- 14.1. Nuclear decay modes.
- 14.2. Binding energy per nucleon.
- 14.3. Proton separation energy.
- 14.4. Neutron separation energy.
- 14.5. Proton pair separation energy.
- 14.6. Neutron pair separation energy.
- 14.7. Error in the von Weizsäcker formula.
- 14.8. Half-life versus energy release in alpha decay.
- 14.9. Schematic potential for an alpha particle that tunnels out of a nucleus.
- 14.10. Half-life predicted by the Gamow / Gurney & Condon theory.
- 14.11. Example average nuclear potentials.
- 14.12. Nuclear energy levels for various average nuclear potentials.
- 14.13. Schematic effect of spin-orbit interaction on the energy levels.
- 14.14. Energy levels for doubly-magic oxygen-16 and neighbors.
- 14.15. Nucleon pairing effect.
- 14.16. Energy levels for neighbors of doubly-magic calcium-40.
- 14.17. 2 excitation energy of even-even nuclei.
- 14.18. Collective motion effects.
- 14.19. Failures of the shell model.
- 14.20. An excitation energy ratio for even-even nuclei.
- 14.21. Textbook vibrating nucleus tellurium-120.
- 14.22. Rotational bands of hafnium-177.
- 14.23. Ground state rotational band of tungsten-183.
- 14.24. Rotational bands of aluminum-25.
- 14.25. Rotational bands of erbium-164.
- 14.26. Ground state rotational band of magnesium-24.
- 14.27. Rotational bands of osmium-190.
- 14.28. Simplified energetics for fission of fermium-256.
- 14.29. Spin of even-even nuclei.
- 14.30. Spin of even-odd nuclei.
- 14.31. Spin of odd-even nuclei.
- 14.32. Spin of odd-odd nuclei.
- 14.33. Selected odd-odd spins predicted using the neighbors.
- 14.34. Selected odd-odd spins predicted from theory.
- 14.35. Parity of even-even nuclei.
- 14.36. Parity of even-odd nuclei.
- 14.37. Parity of odd-even nuclei.
- 14.38. Parity of odd-odd nuclei.
- 14.39. Parity versus the shell model.
- 14.40. Magnetic dipole moments of the ground-state nuclei.
- 14.41. 2 magnetic moment of even-even nuclei.
- 14.42. Electric quadrupole moment.
- 14.43. Electric quadrupole moment corrected for spin.
- 14.44. Isobaric analog states.
- 14.45. Energy release in beta decay of even-odd nuclei.
- 14.46. Energy release in beta decay of odd-even nuclei.
- 14.47. Energy release in beta decay of odd-odd nuclei.
- 14.48. Energy release in beta decay of even-even nuclei.
- 14.49. Examples of beta decay.
- 14.50. The Fermi integral.
- 14.51. Beta decay rates.
- 14.52. Beta decay rates as fraction of a ballparked value.
- 14.53. Parity violation.
- 14.54. Energy levels of tantalum-180.
- 14.55. Half-life of the longest-lived even-odd isomers.
- 14.56. Half-life of the longest-lived odd-even isomers.
- 14.57. Half-life of the longest-lived odd-odd isomers.
- 14.58. Half-life of the longest-lived even-even isomers.
- 14.59. Weisskopf ballpark half-lifes for electromagnetic transitions.
- 14.60. Moszkowski ballpark half-lifes for magnetic transitions.
- 14.61. Comparison of electric gamma decay rates with theory.
- 14.62. Comparison of magnetic gamma decay rates with theory.
- 14.63. Comparisons of decay rates between the same initial and final states.
- A.1. Analysis of conduction.
- A.2. An arbitrary system energy eigenfunction for 36 distinguishable particles.
- A.3. An arbitrary system energy eigenfunction for 36 identical bosons.
- A.4. An arbitrary system energy eigenfunction for 33 identical fermions.
- A.5. Wave functions for a system with just one type of single particle state.
- A.6. Creation and annihilation operators with just one single particle state.
- A.7. Effect of coordinate system rotation on spherical coordinates
- A.8. Effect of coordinate system rotation on a vector.
- A.9. Example energy eigenfunction for the particle in free space.
- A.10. Example energy eigenfunction for a constant accelerating force field.
- A.11. Example energy eigenfunction for a constant decelerating force field.
- A.12. Example energy eigenfunction for the harmonic oscillator.
- A.13. Example energy eigenfunction for a brief accelerating force.
- A.14. Example energy eigenfunction for a particle tunneling through a barrier.
- A.15. Example energy eigenfunction for tunneling through a delta function barrier.
- A.16. Harmonic oscillator potential energy , eigenfunction , and its energy .
- A.17. The Airy Ai and Bi functions.
- A.18. Connection formulae for a turning point from classical to tunneling.
- A.19. Connection formulae for a turning point from tunneling to classical.
- A.20. WKB approximation of tunneling.
- A.21. Scattering of a beam off a target.
- A.22. Graphical interpretation of the Born series.
- A.23. Possible polarizations of a pair of hydrogen atoms.
- A.24. Crude deuteron model.
- A.25. Crude deuteron model with a 0.5 fm repulsive core.
- A.26. Effects of uncertainty in orbital angular momentum.
- A.27. Possible momentum states for a particle confined to a periodic box.
- D.1. Blunting of the absolute potential.
- D.2. Bosons in single-particle-state boxes.
- D.3. Schematic of an example boson distribution on a shelf.
- D.4. Schematic of the Carnot refrigeration cycle.
- N.1. Spectrum for a weak potential.
- N.2. The 17 real wave functions of lowest energy.
- N.3. Spherical coordinates of an arbitrary point P.