linus pauling introduction to quantum mechanics MCGraw hill

00 [r, \ , M area law, 37 G E., 203, 376, 415 y, definition of, MacDonald, ,314 , 101, 228, 385, - *> 282 Klein, 0., 282 Kohlrausch, K^jflT F., 293 Kramers, H A., 198, 282 Kronig, R de L., 276, 293, 390 387 J K L., 188, 189, 353 McDougall, J., 254 MacMillan, W D., 24 Magnetic moment, 412 of electron spin, 208 of hydrogen atom, 147 orbital, 47 Magnetic quantum number, Magnetic susceptibility, 412 Magneton, Bohr, 47 Majorana, E., 353, 359 40, 117 IND&X 462 N Many-electron atoms, 230/ Margenau, H., 386, 387 Matossi, F., 293 Negative J v., 437 Newton's equations, Nielsen, H H., 280, 282 Niessen, K F., 327 prediction of results 66 of, R., of, Modes Mole of vibration of molecules, 287 refraction, definition of, 227 Molecular energy levels, 259 Molecular orbitals, 346 method of, 381 Molecular wave functions, metry properties of, 388 sym- intensities of, 309 Molecules, complex, 366# diatomic, rotation and vibration 263 of, polyatomic, rotation vibration of, 282 quantum number A Moment of, Normalization, of amplitude functions, 89 wave functions, 64 for a continuum, 92 Nucle^ r 37pin for hydrogen, bat of Nu icafnimetry of electronic iraye vjtions for molecules, 39t Nuclear wave function for molecule, 263 Numerical integration, 201 i in, 390 decline of, 48 One-electron bond, 362 of, 14 of, conservation 11 average linear, of electron in hydrogen atom, 146 operator, 54 Momentum wave functions, 436 Morse, P M., 54, 82, 108, 249, 272, 312, 340, 437 function for diatomic molecules, 271 Mott, N F., 83 Mulliken, R S., 346, 381 Multiplication of permutations, definition of, 231 Multiplicity of atomic terms, 220 J Operator, for Hamiltonianp; for angular, r 198 generalized, definition Momentum, ^definition Old qusjitwd diieory, as an approximation to quantum mectyjuiics, 275 of inertia, 269, 275 Momenta, of vibration 287 i Molecule, diatomic, selection rules and Non-degenerate energy level^definition of, 73 Normal coordinates, 282 mode 282 Millikan, R A., 208 Mecke, 392 Neumann, Matrix algebra, 417 Matrix mechanics, 416jf Maximal measurement, 422 Mayer, J E., 229 Mayer, M G., 229 Measurements, states, Nernst, W., 26 Matrices, 417jf momentum, 54 Operators for dynamical quantitu 66 J R., 260 of three-dimenclassical, Orbit, sional oscillator, 11 Oppenheimer, Orbital, definition of, 137 Orbital degeneracy, 367 Orbitals, molecular, 381 Orbits, significance of, i mechanics, 141 Ortho helium, 221 Ortho hydrogen, Orthogonal curviliSBar systems, 441 coordinate >, Orthogonal functions, a convenient set of, 195 IbDEX Orthogonal functions, expansions in terms of, 151 463 for a degenerate level, 165 for non-degenerate levels, 156 defini- Orthogonal transformation, tion of, 288 generalized, 191 prthogonality of wave functions, 64, 89, 441 illation of molecules in crystals, > in polar coor- classical, or, s, _i harmonic, s Larmo*n|, in cylindrical coordinates, 105 in old quantum theory, 30 perturbed, 160 involving the time, in 294-Jf second-order, 176 approximate, 204 Phase integrals in quantum mechanics, 200 Phases of motion, 286 Photochemistry, 26 Photoelectric effect, 25 Photon, 25 Physical constants, values of, 439 Physical interpretation, of harmonic oscillator functions, 73 tjiree-dimensional, in Cartesian ,' of, first-order Perturbation, theory wave equation, 298 wave functions, 63, 88 Pike, H H M., 290 of coordinates, 100 wave mechanics, of oajte-dimensional clap Piaczek, G., 290, 293 Planck, M., 25 Planck's constant, 25 Para hydro[...]... this is to be expected from is process of photoelectric emission involving the conversion of the energy hv of one photon into the kinetic energy of a photoelectron (plus the energy required to remove the quantum theory, the Similarly, Einstein's law of photochemical equivalence states that one molecule may be activated to chemical reaction by the absorption of one photon The third application, to the... the Helium Atoms 44a The Helium Molecule-ion Hef 355 358 358 INTRODUCTION TO QUANTUM MECHANICS CHAPTER I SURVEY OF CLASSICAL MECHANICS The subject of quantum mechanics constitutes the most recent step in the very old search for the general laws_goyrning the motion of matter For a long time investigators confined their studying the dynamics of bodies of macroscopic dimenwhile the science of mechanics. .. agreement with experiments involving atoms and molecules; it was, indeed, just this disagreement which was the principal factor in leading to the development of the atom and later of the quantum mechanics Bohr theory of the Even at the present when an apparently satisfactory theoretical treatment of dynamical systems composed of electrons and nuclei is provided by the quantum mechanics, the problem of the... of axis Angular momenta transform like vectors, the directions of the vectors being the directions of the axes about which the angular momenta are determined It is customary to take the sense of the vectors such as to correspond to the right-hand screw rule 3 THE EQUATIONS OF MOTION IN THE HAMILTONIAN FORM 2a Generalized momentum Momenta In Cartesian related to the direction x k is mx k k, coordinates... Postulates of to the hydrogen The quantum theory had became possible to apply it was not until 1911 that there Bohr developed to this stage before atom; for it it occurred the discovery by Rutherford of the nuclear constitution of the atom its composition from a small heavy positively charged nucleus and one or more extranuclear electrons Attempts were made immediately to apply the quantum theory to The successful... discussed Newton's and then altered their form by purpose, equations in Cartesian coordinates SURVEY OF CLASSICAL MECHANICS 24 [1-4 and potential energies By defining the Lagrangian function for the special case of Newtonian systems and introducing it into the equations of motion, Newton's the introduction of the kinetic equations were then thrown into the Lagrangian form ing an introductory discussion... power of atoms and, in fact, all the chemical properties of atoms and molecules are in explicable in terms of the laws governing the motions of the electrons and nuclei composing them Although it is the modern theory of quantum mechanics in which we are primarily interested because of its applicatiqns _to chemical jjroblems it is desirable for us first to discuss briefly the background of classical mechanics. .. " Theoretical Mechanics Statics and the Dynamics of a Particle," McGraw- Hill Book Company, Inc., New York, 1932 S L LONEY: "Dynamics of a Particle and of Rigid Bodies," Cambridge University Press, Cambridge, 1923 J H JEANS: "Theoretical Mechanics, " Ginn and Company, Boston, 1907 E T WHITTAKER: "Analytical Dynamics," Cambridge University Press, Cambridge, 1928 R C TOLMAN: "Statistical Mechanics with... Hamilton's principle or of the Hamilton-Jacobi partial differential By thus limiting the subjects to be discussed, it is equation possible to give in a short chapter a thorough treatment of Newtonian systems 1 of point particles NEWTON'S EQUATIONS OF MOTION IN THE LAGRANGIAN FORM The is earliest formulation of dynamical laws of wide application If we adopt the notation #-, y Z{ that of Sir Isaac Newton... this survey of classical is important I mechanics is twofold: to indicate the path whereby the more general formulations of classical dynamics, such as the equations of motion of Lagrange first, and of Hamilton, have been developed from the original equations Newton; and second, to illustrate the application of these methods to problems which are later discussed by quantumof mechanical methods In carrying ... vectors, the directions of the vectors being the directions of the axes about which the angular momenta are determined It is customary to take the sense of the vectors such as to correspond to. .. is process of photoelectric emission involving the conversion of the energy hv of one photon into the kinetic energy of a photoelectron (plus the energy required to remove the quantum theory,... Helium Atom Excited States of the Helium Atom The Polarizability of the Normal Helium Atom 29c 29d 29e 221 225 226 CHAPTER IX MANY-ELECTRON ATOMS 30 Slater's 30a 306 30c Treatment of Complex Atoms