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Dr. Lee D. Carlson
- Publié sur Amazon.com
This book goes all the way back to 1930, the year it was first published, and a time when quantum physics was undergoing rapid development, both in terms of applications and theory. The author was one of the major contributors to these developments, and in this book has outlined his idiosyncratic approach to quantum physics, including relativistic quantum mechanics and quantum electrodynamics.The author's insight into quantum physics is extraordinary and that makes this book unique among the books on the subject.
The author introduces immediately the principle of superposition as the tour-de-force of quantum theory in chapter 1 after discussing the inadequacy of classical mechanics in explaining the data on specific heat and atomic spectra. The polarization and interference of photons is used to motivate the principle of superposition, and then the concept of a quantum state. The famous Dirac bra-ket formalism is brought in to give the state concept a mathematical formulation. This is followed in chapter 2 by a mathematical formulation of observables, these being operators that act on the kets, with their adjoints operating on the bras. The eigenvalues of these operators are then the physically realizable results of experiments. The author's discussion on the physical interpretation of this formalism is fascinating and should be read by anyone desiring an in-depth understanding of quantum physics.
The formalism up to this point has been purely algebraic, so to apply it to physical problems one needs a representation. This is done in chapter 3, wherein the author also introduces the famous "Dirac delta function". The commutation relations between observables, not of course arising at all in the classical theory, are discussed in chapter 4. The "Poisson bracket goes to commutator" is the theme of the chapter, and one that was followed for several decades, until the advent of the path integral formulation. The Schroedinger and Heisenberg representations make their appearance here, as well as the Heisenberg uncertainty principle.
Once the ideas of the preceeding chapters are accepted, there is no turning back on the consequences they entail, some of them quite bizarre at first encounter. This already becomes apparent even when solving for the time development of quantum systems, which is done in chapter 10 for the free particle and motion of wave packets.
More applications are treated in chapter 11, such as the harmonic oscillator, and the author shows how to incorporate angular momentum and spin into the quantum theory. He also treats the central force problem, and derives the selection rules for the hydrogen atom. Readers get their first taste of perturbation theory in chapter 12, via the problem of atom in an external electric field. All of these problems illustrate beautifully the ability of quantum physics to fit the experimental data.
Particle accelarators were of course coming on to the scene at the time this book was published, and so collision problems are discussed in chapter 13. The important effects of resonance scattering and spontaneous emission are discussed in detail by the author.
Even more anti-classical phenomena in quantum physics arise in chapter 14, which deals with systems of identical particles. The description of these is done with symmetrical and antisymmetrical states, and the resulting boson/fermion distinction is outlined and discussed in detail. The author also gives an interesting discussion of permutations as dynamical variables. He constructs a theory for a system of n similar particles when states of any kind of symmetry properties are allowed. The theory does not correspond to any existing particles (and the author acknowledges this), but he uses it as an approximation to a collection of electrons. Permutations are constants of motion in this theory, and for a system of electrons he shows that more than two electrons cannot be in the same orbital state. This "effective" theory of electrons is interesting because in its derivation one sees the explicit need for spin variables, even though spin forces are neglected by the author. This is a neat illustration of the Pauli exclusion principle.
In chapter 20, the author develops a theory of radiation, giving a first glance at relativistic quantum theory, i.e. quantum field theory. The theory as he constructs initially however should more properly be called many-body quantum theory, as no explicit "field quantization" is performed, although his result is essentially the same: a collection of quantized harmonic oscillators which he shows to be equivalent to a collection of bosons in stationary states. He applies this theory to the case of a collection of photons interacting with an atom. When describing the interactions between photons and atoms, he then makes the connection with fields, treating the atom first classically and the field of radiation as a vector field. The resulting theory is quantized using the "canonical" approach and the author derives all the now standard quantities, such as the Kramers-Heisenberg dispersion formula for photon scattering.
Dirac is well-known for his work in quantum field theory, and he delves into it in the last two chapters. His famous derivation of the "Dirac equation" is given here, but interestingly, he does not refer to the wave functions in this equation as "spinors". He does show the equation is Lorentz invariant, and then studies the electron in a central force using the equation, giving the all-important fine structure of the energy levels. And of course, the theory of the positron is discussed here. The treatment of quantum electrodynamics is done from a canonical quantization viewpoint, and the discussion of electrons and positrons is now legendary.