Varshalovich Quantum Theory Of Angular Momentum.pdf
this is a book about the intrinsic angular momentum of a free particle. it is an account of two independent approaches to quantum mechanics applied to the spin, both in the familiar fock space, and also in the more abstract hilbert space. the approaches to the free particle are completely equivalent. all of the intrinsic quantities of the particle are described in terms of the operator sum over states of the fock space. the intrinsic operator is not a self-adjoint operator, but is unitarily equivalent to the diagonal operator of the conventional fock space. the hilbert space approach includes just the bare angular momentum, and not the intrinsic spin. the two approaches are compared with each other and with the dirac theory, in detail. the most important results are summarized.
this book deals with the basic concepts of quantum mechanics and quantum field theory. the starting point is a discussion of the connection between classical and quantum mechanics and the derivation of classical mechanics from schrödinger’s equation for a single particle in the framework of wave mechanics. we then go on to consider the consequences of a quantization of classical mechanics. the wave function of a system is represented as a linear combination of basis vectors of a hilbert space and the rules of the mathematical formalism of quantum mechanics follow from the properties of this space. the process of quantization should be distinguished from the process of renormalization which leads to an infinite series of diverging quantities. the main points of the latter are summarized. we close the book with a discussion of quantum field theory, the main difference of which from classical mechanics is the appearance of a space-time structure. our goal is to give a plain, coherent introduction to quantum mechanics and quantum field theory. each chapter ends with a list of theorems and formulae necessary for the next chapter. the book contains no figures, except those which are embedded in tables.
this book explores the nature of particles on the basis of current understanding of symmetries, groups and their representations. it begins with a review of particle physics and elementary particles physics and makes an attempt to show why many symmetries that are usually present in the description of interacting fields are absent in theories of free particles. it also explains the significance of the properties of symmetry group in the creation and destruction of elementary particles. the difference between the symmetries of galilean and lorentz transformations becomes clear. the electromagnetic potential vector is shown to have the symmetry of the lorentz transformation. the symmetries of spin and charge are also discussed with emphasis on the fact that they have a purely group-theoretic foundation. the concepts of energy, mass, and momentum of free particles are also discussed.
expressions similar to those cited in this work are encountered in many branches of physics, such as classical mechanics, celestial mechanics, electrical and magnetic engineering, optics, spectroscopy, quantum optics, quantum mechanics, nuclear physics and atomic physics. applications in physics and chemistry are numerous and range from simple problems to the study of more advanced dynamical systems.
eigenfunctions of a particle with a central electric charge of the n- th power may be constructed from products of the angular part of the coulomb wave function and eigenfunctions of the internal spherical harmonics. the radial wave functions of these two parts are related. in this way we present a method to derive the solutions of this problem in the form of a formula similar to the one in (3.71). they are referred to as the generalized coulomb wave functions. this method is quite general and may be used for obtaining the eigenfunctions for any central potential. the eigenfunctions are possible for any n. their angular dependencies are based on the legendre polynomials. the 3n dependency is characterized by the projection quantum number l. examples are given for the relativistic harmonic oscillator, p&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt;1/2&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;gt; potential, the oscillator potential, the harmonic oscillator potential, the morse potential and more complex potentials such as the asymmetric potential, the one-dimensional euclidean potential and the rotation potential. examples of physical systems are provided, such as the hydrogen atom, the coulomb potential, the p&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;lt;1/2&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;gt; atomic nucleus, the coulomb + coulomb potential and the morse + coulomb potential. eigenvalues and eigenfunctions are given explicitly. the method also yields the wave functions and eigenvalues for the hydrogen atom. the formula for the wave functions and eigenvalues of this problem is given in (6.11). they are referred to as the generalized radial harmonic oscillator wave functions. these states are represented by their corresponding laguerre polynomials. this method may be used to calculate the energy levels of the hydrogen atom. consequences for the hydrogen atom spectrum, in the case of no electric field, are presented.