Quantum Mechanics Made Simple: Lecture Notes

Quantum mechanics (or quantum physics) is an important intellectual achievement of the 20th century. It is one of the more sophisticated fields in physics that has affected our understanding of nano-meter length scale systems important for chemistry, materials, optics, electronics, and quantum information. The existence of orbitals and energy levels in atoms can only be explained by quantum mechanics. Quantum mechanics can explain the behaviors of insulators, conductors, semiconductors , and giant magneto-resistance. It can explain the quantization of light and its particle nature in addition to its wave nature (known as particle-wave duality). Quantum mechanics can also explain the radiation of hot body or black body, and its change of color with respect to temperature. It explains the presence of holes and the transport of holes and electrons in electronic devices. The first observation of something quantum was probably by Michael Faraday in 1838 on cathode rays: the fact that when electrons bombard a cathode, light is given out. The next quantum phenomenon was the black body radiation of Gustav Kirchhoff in 1859-1860. Ludwig Boltzmann conjectured that atomic energy levels should be discrete around 1877. Heinrich Hertz first observed the photo-electric effect in 1887 which was later explained by Einstein in 1905 using the particle nature of light. Examples of famous physicists that contribute to quantum mechanics were Planck proposed the Planck radiation law in 1900 that I(ν) = 2hν 3 c 2 1 e hν/k b T − 1 (1.1.1) where h ≈ 6.626 × 10 −34 J · s is Planck constant, c is velocity of light, ν the frequency of light, k b = 1.38064852(79) × 10 −23 J/K is Boltzmann constant, and T the temperature in Kelvin. The above radiation law is obtained by assuming that light forms quanta of energy each of which is given by hν when the quantum theory of light was not well understood. When the Planck constant becomes negligibly small, implying that the quantization of light 1 2 Quantum Mechanics Made Simple is unimportant, the above formula becomes I(ν) ≈ 2ν 2 c 2 k b T (1.1.2) which becomes Rayleigh-Jeans law of radiation. This law fails to predict radiation of a black body correctly when the frequency is high. Figure 1.1: Planck black body radiation law: With decreasing temperature, the peak of the black body radiation curve shifts to longer wavelengths and also has lower intensities. The black body …