1. 1 2. Atoms and Electrons How to describe a new physical phenomenon? New natural phenomenon Previously existing theory Not explained Explained New theoryPredicts new phenomena Experiments confirm new phenomena

2. 2 How to describe a new physical phenomenon? New phenomenon Previous Theory New comprehensive theory

3. 3 Shortest Course in Quantum Mechanics Observation: Electrons and atoms did not obey the classical laws of mechanics. New theory: Quantum mechanics predicts the way in which electrons behave in solids.. Postulate: The light is quantized. The smallest discrete unit of energy is photon. E=h·f h=6.625*10 Js Planck constant E – Energy of photon f – Frequency of light -34

4. 4 Shortest Course in Quantum Mechanics, Cont. Nobel Prizes: 1918 Planck for the discovery of energy quanta 1921 Einstein for the law of the photoelectric effect Dual nature: Wave Particle Light: Wave nature: electromagnetic wave f=1/ T (Hz) =c/f (m) wavelength Particle nature : photon p=h/ momentum of a photon

5. 5 Shortest Course in Quantum Mechanics, Cont. Atomic spectra: Bohr model of atom Nobel prize 1922 Niels Bohr for structure of atoms and radiation emanating from them Bohr postulates: 1)Electron exists in certain stable circular orbits about the nucleus and does not give off radiation 2)Electron may shift to an orbit of higher or lower energy by absorbing or emitting a photon of energy hf 3)Angular momentum is quantized p =m v r = n h/2  

6. 6 Atomic spectra: Bohr model of atom Shortest Course in Quantum Mechanics, Cont. e- hf = E 3 -E 1 Emission e- hf =E 2 -E 1 Absorption 1 2 3 31 12 E E E

7. 7 Shortest Course in Quantum Mechanics, Cont. Heisenberg Uncertainty Principle (Nobel prize 1932 for the creation of quantum mechanics) The more precise you know the position of a particle, the less precise you know the momentum of the particle:  x  p x ≥ h/2  The more precise you know the time, the less precise you know the energy:  E  t ≥ h/2 

8. 8 Shortest Course in Quantum Mechanics, Cont. Schrodinger Wave Equation Dual nature of Electron : Wave: Wave function  (x) Schrodinger Wave Equation  (x)  * (x) dx is probability that the position of electron is within (x, x+  x) Particle: Mass Position Momentum Energy

9. 9 Shortest Course in Quantum Mechanics, Cont. Schrodinger equation and solution for the potential well problem will be presented in class.