List of Fig­ures

• 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 $\psi_{111}$ and $\psi_{211}$ 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 $\psi_{100}$ and $\psi_{010}$.
• 4.5. En­ergy eigen­func­tion $\psi_{213}$.
• 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 $\psi_{200}$.
• 4.11. Eigen­func­tion $\psi_{210}$, or 2p$_z$.
• 4.12. Eigen­func­tion $\psi_{211}$ (and $\psi_{21-1}$).
• 4.13. Eigen­func­tions 2p$_x$, left, and 2p$_y$, right.
• 4.14. Hy­dro­gen atom plus free pro­ton far apart.
• 4.15. Hy­dro­gen atom plus free pro­ton closer to­gether.
• 4.16. The elec­tron be­ing an­ti­sym­met­ri­cally 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 hy­dro­gen and he­lium.
• 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$_z$ states.
• 5.10. Co­va­lent pi bond con­sist­ing of two 2p$_x$ states.
• 5.11. Co­va­lent sigma bond con­sist­ing of a 2p$_z$ and a 1s state.
• 5.12. Shape of an sp$^3$ hy­brid state.
• 5.13. Shapes of the sp$^2$ 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 en­ergy eigen­func­tion for a sim­ple sys­tem.
• 6.6. State with 5 times the sin­gle-par­ti­cle ground state en­ergy.
• 6.7. Dis­tin­guish­able par­ti­cles: eigen­func­tions for dis­tri­b­u­tion A.
• 6.8. Dis­tin­guish­able par­ti­cles: 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 $y$-di­rec­tion.
• 6.13. Se­vere con­fine­ment in both the $y$ and $z$ 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 vol­ume.
• 6.17. Ground state of non­in­ter­act­ing elec­trons in a pe­ri­odic box.
• 6.18. Con­duc­tion in the free-elec­tron gas model.
• 6.19. Sketch of elec­tron spec­tra in solids at zero tem­per­a­ture.
• 6.20. Sketch of elec­tron spec­tra in solids at 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. One-di­men­sional en­ergy bands for 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 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 a 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 eigen­func­tions 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. Be­fore the Venus mea­sure­ment and im­me­di­ately af­ter it.
• 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. Re­defin­ing the oc­cu­pied wave num­bers 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 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 eigen­func­tions for a 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 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 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 in­di­cates net charge.
• 13.4. The net num­ber of out­go­ing mag­netic field lines is 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 mag­netic field ro­tat­ing at the Lar­mor fre­quency.
• 14.1. Chart of the nu­clides.
• 14.2. Nu­clear de­cay modes.
• 14.3. Nu­clear half-lifes.
• 14.4. Bind­ing en­ergy per nu­cleon.
• 14.5. Pro­ton sep­a­ra­tion en­ergy.
• 14.6. Neu­tron sep­a­ra­tion en­ergy.
• 14.7. Pro­ton pair sep­a­ra­tion en­ergy.
• 14.8. Neu­tron pair sep­a­ra­tion en­ergy.
• 14.9. Er­ror in the von Weizsäcker for­mula.
• 14.10. Half-life ver­sus en­ergy re­lease in al­pha de­cay.
• 14.11. Schematic po­ten­tial for a tun­nel­ing al­pha par­ti­cle.
• 14.12. Half-life pre­dicted by the Gamow / Gur­ney & Con­don the­ory.
• 14.13. Ex­am­ple av­er­age nu­clear po­ten­tials.
• 14.14. Nu­clear en­ergy lev­els for var­i­ous av­er­age nu­clear po­ten­tials.
• 14.15. Schematic ef­fect of spin-or­bit in­ter­ac­tion on the en­ergy lev­els.
• 14.16. En­ergy lev­els for dou­bly-magic oxy­gen-16 and neigh­bors.
• 14.17. Nu­cleon pair­ing ef­fect.
• 14.18. En­ergy lev­els for neigh­bors of dou­bly-magic cal­cium-40.
• 14.19. 2$^+$ ex­ci­ta­tion en­ergy of even-even nu­clei.
• 14.20. Col­lec­tive mo­tion ef­fects.
• 14.21. Fail­ures of the shell model.
• 14.22. An ex­ci­ta­tion en­ergy ra­tio for even-even nu­clei.
• 14.23. Text­book vi­brat­ing nu­cleus tel­lurium-120.
• 14.24. Ro­ta­tional bands of hafnium-177.
• 14.25. Ground state ro­ta­tional band of tung­sten-183.
• 14.26. Ro­ta­tional bands of alu­minum-25.
• 14.27. Ro­ta­tional bands of er­bium-164.
• 14.28. Ground state ro­ta­tional band of mag­ne­sium-24.
• 14.29. Ro­ta­tional bands of os­mium-190.
• 14.30. Sim­pli­fied en­er­get­ics for fis­sion of fer­mium-256.
• 14.31. Spin of even-even nu­clei.
• 14.32. Spin of even-odd nu­clei.
• 14.33. Spin of odd-even nu­clei.
• 14.34. Spin of odd-odd nu­clei.
• 14.35. Odd-odd spins pre­dicted us­ing the neigh­bors.
• 14.36. Odd-odd spins pre­dicted from the­ory.
• 14.37. Par­ity of even-even nu­clei.
• 14.38. Par­ity of even-odd nu­clei.
• 14.39. Par­ity of odd-even nu­clei.
• 14.40. Par­ity of odd-odd nu­clei.
• 14.41. Par­ity ver­sus the shell model.
• 14.42. Mag­netic di­pole mo­ments of the ground-state nu­clei.
• 14.43. 2$^+$ mag­netic mo­ment of even-even nu­clei.
• 14.44. Elec­tric quadru­pole mo­ment.
• 14.45. Elec­tric quadru­pole mo­ment cor­rected for spin.
• 14.46. Iso­baric ana­log states.
• 14.47. En­ergy re­lease in beta de­cay of even-odd nu­clei.
• 14.48. En­ergy re­lease in beta de­cay of odd-even nu­clei.
• 14.49. En­ergy re­lease in beta de­cay of odd-odd nu­clei.
• 14.50. En­ergy re­lease in beta de­cay of even-even nu­clei.
• 14.51. Ex­am­ples of beta de­cay.
• 14.52. The Fermi in­te­gral.
• 14.53. Beta de­cay rates.
• 14.54. Beta de­cay rates as frac­tion of a ball­parked value.
• 14.55. Par­ity vi­o­la­tion.
• 14.56. En­ergy lev­els of tan­ta­lum-180.
• 14.57. Half-life of the longest-lived even-odd iso­mers.
• 14.58. Half-life of the longest-lived odd-even iso­mers.
• 14.59. Half-life of the longest-lived odd-odd iso­mers.
• 14.60. Half-life of the longest-lived even-even iso­mers.
• 14.61. Weis­skopf ball­park half-lifes for elec­tro­mag­netic tran­si­tions.
• 14.62. Moszkowski ball­park half-lifes for mag­netic tran­si­tions.
• 14.63. Com­par­i­son of elec­tric gamma de­cay rates with the­ory.
• 14.64. Com­par­i­son of mag­netic gamma de­cay rates with the­ory.
• 14.65. De­cay rates be­tween the same ini­tial and fi­nal states.
• A.1. Analy­sis of con­duc­tion.
• A.2. A sys­tem eigen­func­tion for 36 dis­tin­guish­able par­ti­cles.
• A.3. A sys­tem en­ergy eigen­func­tion for 36 iden­ti­cal bosons.
• A.4. A sys­tem en­ergy eigen­func­tion for 33 iden­ti­cal fermi­ons.
• A.5. Wave func­tions with just one type of sin­gle par­ti­cle state.
• A.6. Cre­ation and an­ni­hi­la­tion op­er­a­tors for 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 an ac­cel­er­at­ing force.
• A.11. Ex­am­ple en­ergy eigen­func­tion for a de­cel­er­at­ing force.
• 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 tun­nel­ing through a bar­rier.
• A.15. Tun­nel­ing through a delta func­tion bar­rier.
• A.16. Har­monic os­cil­la­tor po­ten­tial en­ergy and ex­am­ple eigen­func­tion.
• A.17. The Airy Ai and Bi func­tions.
• A.18. Con­nec­tion for­mu­lae for go­ing from nor­mal to tun­nel­ing.
• A.19. Con­nec­tion for­mu­lae for go­ing from tun­nel­ing to nor­mal.
• 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 in 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.