More than one hundred years since its discovery quantum mechanics remains today as beautiful in its unifying simplicity, accurate in its experimental predictions, and strange in its metaphysical implications as ever. Quantum mechanics treats particles of matter on an equal footing with light, thus unifying hitherto disparate physical phenomena. Schrodinger’s equation gives a remarkably accurate picture of the hydrogen atom, which leads to the periodic table of elements. In quantum mechanics, the momentum, the energy, and even the position of a particle are no longer determinate, rather they are random variables giving only probabilities until we intervene to make an observation.
This book contains an exposition of core topics from quantum mechanics along with a separate chapter on mathematical prerequisites. An observable of a physical system is defined as a random variable. From this definition the Heisenberg uncertainty principle is seen as a result from probability theory, giving a lower bound on the product of the standard deviations of two incompatible observables. Examples and implications of the uncertainty principle are discussed: the time-energy uncertainty principle is seen as a possible explanation of the phenomenon of quantum vacuum fluctuations; the so-called coherent quantum states are seen as uncertainty minimizing states. Schrodinger’s equation with a spherically symmetric potential is discussed in detail: as an application the hydrogen atom is analyzed, which then leads to the notions of quantum numbers and quantized energy levels. The spin of a particle is postulated in analogy with the angular momentum of a particle. The wave function of an electron complete with its spin state is analyzed, which quickly leads to the periodic table of elements. Quantum statistical mechanics underlying the difference between fermions and bosons is explained. The quantum harmonic oscillator and its many applications are given. In particular, the algebraic solution is used to quantize the classical or nonrelativistic electromagnetism. This formulation leads to the phenomenon of photon emission and absorption by an atom, thus laying a foundation for quantum field theory.
This book contains an exposition of core topics from quantum mechanics along with a separate chapter on mathematical prerequisites. An observable of a physical system is defined as a random variable. From this definition the Heisenberg uncertainty principle is seen as a result from probability theory, giving a lower bound on the product of the standard deviations of two incompatible observables. Examples and implications of the uncertainty principle are discussed: the time-energy uncertainty principle is seen as a possible explanation of the phenomenon of quantum vacuum fluctuations; the so-called coherent quantum states are seen as uncertainty minimizing states. Schrodinger’s equation with a spherically symmetric potential is discussed in detail: as an application the hydrogen atom is analyzed, which then leads to the notions of quantum numbers and quantized energy levels. The spin of a particle is postulated in analogy with the angular momentum of a particle. The wave function of an electron complete with its spin state is analyzed, which quickly leads to the periodic table of elements. Quantum statistical mechanics underlying the difference between fermions and bosons is explained. The quantum harmonic oscillator and its many applications are given. In particular, the algebraic solution is used to quantize the classical or nonrelativistic electromagnetism. This formulation leads to the phenomenon of photon emission and absorption by an atom, thus laying a foundation for quantum field theory.
