that such small light particles behaved in a way that simply is not consistent with the Newton equations. Let me now illustrate some of the experimental data that gave rise to these paradoxes and show you how the scientists of those early times then used these data o suggest new equations that these particles might obey. I want to stress that the Schrodinger equation was not derived but postulated by these scientists. In fact, to date, no one has been able to derive the Schrodinger equation From the pioneering work of Bragg on diffraction of x-rays from planes of atoms or ions in crystals, it was known that peaks in the intensity of diffracted x-rays having wavelength n would occur at scattering angles 0 determined by the famous Bragg equati n入=2dsin where d is the spacing between neighboring planes of atoms or ions. These quantities are illustrated in Fig. 1. I shown below. There are may such diffraction peaks, each labeled by a different value of the integer n(n=1, 2, 3,). The Bragg formula can be derived by considering when two photons, one scattering from the second plane in the figure and the second scattering from the third plane, will undergo constructive interference. This condition is met when the extra path length"covered by the second photon (i.e, the length from points a to B to C)is an integer multiple of the wavelength of the photons2 that such small light particles behaved in a way that simply is not consistent with the Newton equations. Let me now illustrate some of the experimental data that gave rise to these paradoxes and show you how the scientists of those early times then used these data to suggest new equations that these particles might obey. I want to stress that the Schrödinger equation was not derived but postulated by these scientists. In fact, to date, no one has been able to derive the Schrödinger equation. From the pioneering work of Bragg on diffraction of x-rays from planes of atoms or ions in crystals, it was known that peaks in the intensity of diffracted x-rays having wavelength l would occur at scattering angles q determined by the famous Bragg equation: n l = 2 d sinq, where d is the spacing between neighboring planes of atoms or ions. These quantities are illustrated in Fig. 1.1 shown below. There are may such diffraction peaks, each labeled by a different value of the integer n (n = 1, 2, 3, …). The Bragg formula can be derived by considering when two photons, one scattering from the second plane in the figure and the second scattering from the third plane, will undergo constructive interference. This condition is met when the “extra path length” covered by the second photon (i.e., the length from points A to B to C) is an integer multiple of the wavelength of the photons