2. 2 x 3 = 6

3. and of course 3 x 2 = 6

4. 2 x 3 = 6 and of course 3 x 2 = 6 But in the Quantum World things can happen that are not so obvious

5. 2 x 3 = 6 and of course 3 x 2 = 6 But in the Quantum World things can happen that are not so obvious sometimes a x b  b x a

6. Harry Kroto 2004

11. The same laws apply also when photons hit light receptors in our eyes

12. ©

13. J H Van Vleck ©

26. 2 x 3 = 6 and of course 3 x 2 = 6 But in the Quantum World things can happen that are not so obvious sometimes a x b  b x a

27. 2 x 3 = 6 and of course 3 x 2 = 6 But in the Quantum World things can happen that are not so obvious sometimes a x b  b x a

28. Harry Kroto 2004

37. J H Van Vleck ©

38. ©

39. J a J b – J b J a = -iJ c

40. ©

41. The Quantum Mechanical equation for angular momentum J x J y – J y J x = iJ z explains the electron motion and the Periodic Table

42. commutation 3x4 – 4x3 = 0 but sometimes AxB – BxA  0 Called non-commutation

43. commutation 3x4 – 4x3 = 0 but sometimes AxB – BxA  0 Called non-commutation

44. commutation 3x4 – 4x3 = 0 but sometimes AxB – BxA  0 Called non-commutation

45. J H Van Vleck ©

46. ©

47. [J 2,[J 2,T]] = [J 2,(J 2 T – TJ 2 )] = J 4 T – 2J 2 TJ 2 + TJ 4 When light is absorbed or emitted the elegant Dirac relation governs the process

48. J H Van Vleck ©

49. The Quantum Mechanical equation for angular momentum J x J y – J y J x = iJ z ©

50. J H Van Vleck ©

51. The Quantum Mechanical equation for angular momentum J x J y – J y J x = iJ z but 3x4 – 4x3 = 0 !!!!!!! ©

52. So what are these funny things J x, J y and J z ©

53. RR R R

54. RR R R 

55. [J 2,[J 2,T] = [J 2,(J 2 T – TJ 2 )] = J 4 T – 2J 2 TJ 2 + TJ 4 LIGHT When a hydrogen atom in the Sun’s atmosphere emits a photon of light, an electron makes a jump from one energy state to another and elegant magical equations such as worked out by Paul Dirac, govern the process and the way the photon – after bouncing off an object is detected by your eye. So, the way we see and receive all visual information is governed by such beautiful relations. To fully appreciate these mysteries we have to be able to understand some mathematics.

56. [J 2,[J 2,T] = [J 2,(J 2 T – TJ 2 )] = J 4 T – 2J 2 TJ 2 + TJ 4 LIGHT When a hydrogen atom in the Sun’s atmosphere emits a photon of light, an electron makes a jump from one energy state to another and elegant magical equations such as worked out by Paul Dirac, govern the process and the way the photon – after bouncing off an object is detected by your eye. So, the way we see and receive all visual information is governed by such beautiful relations. To fully appreciate these mysteries we have to be able to understand some mathematics.

57. [J 2,[J 2,T] = [J 2,(J 2 T – TJ 2 )] = J 4 T – 2J 2 TJ 2 + TJ 4 LIGHT When a hydrogen atom in the Sun’s atmosphere emits a photon of light, an electron makes a jump from one energy state to another and elegant magical equations such as worked out by Paul Dirac, govern the process and the way the photon – after bouncing off an object is detected by your eye. So, the way we see and receive all visual information is governed by such beautiful relations. To fully appreciate these mysteries we have to be able to understand some mathematics.

58. [J 2,[J 2,T] = [J 2,(J 2 T – TJ 2 )] = J 4 T – 2J 2 TJ 2 + TJ 4 When light is absorbed the Dirac equation governs the process