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Taketani M. The formation and logic of quantum mechanics
Taketani M.  The formation and logic of quantum mechanics


: The formation and logic of quantum mechanics

: Taketani M.


This book analyzes the intricate logical process through which the quantum theory was developed, and shows that the quantum mechanics thus established is governed by stereo-structural logic. The method of analysis is based on Mituo Taketani's three-stage theory of scientific cognition, which was presented and developed in close connection with Yukawa's theory of the meson. According to the three-stage theory, scientific cognition proceeds through a series of coiling turns of the phenomenological, substantialistic and essentialistic stages. The old quantum mechanics is shown to be in a substantialistic stage, followed by the quantum mechanics in the corresponding essentialistic stage.

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$g$-factor, anomaly in s-terms of      II183 189 191
$g$-factor, introduciton by Lande of      II182
$g$-factor, of multiplet terms      II188
$g$-factor, problem of the relativistic correction of      II213
$q$-algebraic treatment of angular momentum      III53
$q$-algebraic treatment of equation of electron orbit      III50
$q$-number, Diracs      III47
$q$-number, matrix element and representation of      III50
$X$-ray doublet terms, regular and irregular      II205
$X$-ray doublet terms, screening and relativistic      II205
$X$-ray doublet terms, similarity to optical doublet terms of      II209
$\alpha$-rays, detection of large-angle scattering of      203
Abraham angular momentum carried away by radiation      II159
Abraham magnetic moment of rotating spherical electron      II220
Adams      II81
Adiabatic hypothesis, and correspondence principle      II166
Adiabatic hypothesis, as generalization of Wiens displacement law      II165
Adiabatic hypothesis, Ehrenfests      II165
Adiabatic invariant, indication of existence of      II165
Allen      II221
Andrade      see Rutherford-
Andrade e Silva      see de Broglie-
Angular momentum, $q$-algebraic, treatment of      III53
Angular momentum, Bohrs assumption of constancy of      II93
Angular momentum, carried away by radiation      II159
Angular momentum, conservation law and selection rules of      II158
Angular momentum, indication of quantum nature of (Nicholson)      II77
Angular momentum, of atomic body      II184 187
Angular momentum, properties in matrix mechanics of      III29
Angular momentum, quantum nature in Bohr model of      II92
Angular momentum, relativistic limit of (Sommerfeld)      II126
Anomalous Zeeman effect and half-integer quantum number      II182
Anomalous Zeeman effect and Runges rule      II181
Anomalous Zeeman effect and Stern Gerlachs experiment      II195
Anomalous Zeeman effect, systematization by Back of      II182
Anomalous Zeeman effect, treatment by matrix mechanics of      III31
Anomaly of $g$-factor of $s$-terms and magneto-mechanical anomaly      II1783 190 191
Anomaly of $g$-factor of $s$-terms and magneto-optical anomaly      II189
Anticommutation relation for de Broglie waves obeying F D statistics (Jordan Wigner)      III225
Aperiodic motion, attempt at application of matrix mechanics to      III61 125
Aperiodic motion, difficulty in applying quantum condition to      II195
Aperiodic motion, generalization of matrix mechanics to      III174
Arrhenius      097
Arvidsson      II191
Avogadro number, Thomsons determination (by method of electrolysis) of      0112
Azimuthal quantum number, Sommerfelds introduction of      II123
Azimuthal quantum number, two kinds of (Bohr Coster)      II206
Back      see Pascen-
Back systematization of anomalous Zeeman effect      II182
Balmer formula, derivation using Bohr model of      II88
Balmer formula, Diracs discussion based on $q$-algebra of      III52
Balmer formula, Ishiwaras derivation of a formula similar to      II113
Balmer formula, Paulis matrix mechanical derivation of      III37
Balmer formula, Schr$\ddot{o}$dingers wave mechanical derivation of      III76
Balmer formula, Sommerfelds derivation from the quantum condition of      II118
Balmer presentation of spectral formula      063
Barkla determination of number of centers of X-ray scattering in atoms      0183
Barkla study of secondary X-rays      0180 183
Barnet      II191
Bates      see Sucksmith-
Beck      II191
BKS theory      see Bohr Kramers Slater
Black body radiation Kirchhoffs concept and law of      05
Bohr assumption of constancy of angular momentum      II93
Bohr assumption of quantum numbers invariance      II218
Bohr configuration of inner-atomic electrons      II98 202
Bohr determination of number of electron in hydrogen atom      0229
Bohr doubt on energy-momentum conservation      II263
Bohr doubt on half-integral quantum numbers      II208
Bohr frequency condition      II87 151 III20
Bohr germ of correspondence principle      II92
Bohr inference of frequency of inner-atomic electrons      II81
Bohr interpretation of Franck Hertzs experiment      II102
Bohr model and quantum nature of angular momentum      II93
Bohr model and radius of hydrogen atom      II84
Bohr model and structures of atom and molecule      II94
Bohr model and the spectral formula      II88
Bohr model, basic assumptions of      II86
Bohr model, confirmation by Mosely of      II99
Bohr nonmechanical compulsion to lighting electrons      II209 216 III103
Bohr presentation of Bohr model of atom      II82
Bohr presentation of correspondence principle      II163
Bohr reply to EPRs question      III282
Bohr support for negation of causality      III248
Bohr treatment of Stark and Zeeman effects by a pre-correspondence-principle      II143
Bohr use of the term complementarity      III248 249
Bohr Coster introduction of two kinds of azimuthal quantum numbers      II206
Bohr Kramers Slater idea of virtual oscillation      II267 275
Bohr Kramers Slater theory of statistical conservation of energy-momentum      II266
Boltzmann      see Stefan-
Born approximation, Wentzels application to Rutherford scattering      III198
Born dispersion formula      II277
Born introduction of concept of probability into wave mechanics      III129 152
Born reversibility of transition probability      III165
Born transition probability (of absorption and induced emission)      III164
Born Heisenberg Jordan, introduction of canonical transformation      III27
Born Heisenberg Jordan, matrix mechanics of a string      III35
Born Heisenberg Jordan, matrix mechanics of a system of multi-degrees of freedom      III26
Born Heisenberg Jordan, matrix mechanics of angular momentum      III29
Born Heisenberg Jordan, perturbation method in matrix mechanics      III28
Born Heisenberg Jordan, relative intensity in Zeeman effect      III30
Born Jordan, attempt to treat the electro-magnetic equations by matrix mechanics      III33
Born Jordan, equation of motion in matrix mechanics      III26
Born Jordan, intensified quantum condition      III23
Born Jordan, matrix mechanics of systems of one degree of freedom      III19
Born Jordan, matrixization of canonical equations of motion      III21
Born Jordans quantum condition and the commutation relation      III22
Born K$\acute{a}$rm$\acute{a}$n theory of specific heats of solids      1124
Born Wiener attempt at applying matrix mechanics to aperiodic moeiton      III61 189
Born, The Born approximation (of scattering probability)      III135
Bose statistical mechanics of gas of light quanta      II253
Bose Einstein statistics      II258 III152
Bothe Geiger experiment nagating the BKS theory      II269
Boundary between an object and apparatus of observation      III261 274 275
Bowen      see Millikan-
Brackett spectral series of      164
Breit idea of virtual orbit      II275
Brillouin, L., WKB approximation of wave equation      III92
Brillouin, M., inner-atomic elastic waves and quantum condition      II244
Burgers      II166
Busch angular momentum carried away by radiation      II159
Campbell      II199
Canonical transformation and wave mechanics (London)      III167
Canonical transformation in matrix mechanics      III27
Canonical transformation, Diracs transformation theory based on      III175
Catal$\acute{a}$n      II186
Catalog of expectation, wave function as (Schrodinger)      III269
Clark Duane anomalous scattering of X-rays      II239
Combination rule of amplitudes (classical)      III10
Combination rule of amplitudes (quantum-theoretical)      III10 20
Combination rule of frequency (classical)      III8
Combination rule of frequency (quantum-theoretical)      III8 20
Combination rule of spectral lines (Ritz)      1163
Commutation relation and anticommutation relation      III225
Commutation relation and Born Jordans intensified quantum condition      III23
Commutation relation and Diracs Poisson bracket equation      III47
Commutation relation and Heisenbergs quantum-theoretical quantum condition      III23
Commutation relation and the uncertainty relation      III241
Commutation relation of angular momenta      III29
Complementarity in Bohrs wording      III247 249
Complementarity, Taketanis critique of      III252
Complexion number and com-bination with repetition      II257
Complexion number and the derivation by Debye of the Planck formula      1118
Complexion number, Plancks      128 1114
Compton effect, Diracs Aplication of matrix mechanics to      III203
Compton effect, Gordons application of wave mechanics to      III203
Compton effect, interpretation according to the BKS theory of      II268
Compton effect, Klein Nishninas application of Diracs electron wave equation to      III232
Compton effect, Tamms application of quantum field theory to      III233
Compton Simon experiment negating the BKS theory      II270
Compton, light quanta and reflection and diffraction of X-rays      II242
Compton, scattering of X-rays and size of electron      II235
Compton, spin and the magneto-mechanical anomaly      II221
Compton, theory and experiment of Compton effect      II236
Condon, commutation relation and the uncertainty relation      III241
Conflict between field and matter Indication by Taketani of      II225 III235
Conjugate configuration about a closed shell      II217
Conservation law of energy-momentum, doubts by Bohr of      II263
Conservation law of energy-momentum, statistical      II256
Continuity equation of charge density (Schrodinger)      III123
Continuity equation of four-current density (Klein, Gordon)      III203
Contradiction in radiation theory Indication by Einstein of      149 117
Copenhagen spirit, cause of vagueness of      III274
Copenhagen spirit, in interpretation of quantum mechanics      III252
Corpuscle, name of electron (Thomson)      1115
Corpuscle, Thomsons model of atoms without nucleus by means of      1106 128 140
Correspondence principle and intensity of radiation      II169
Correspondence principle and selection rule      II163
Correspondence principle and the adiabatic hypothesis      II166
Correspondence principle, germ of      1192
Correspondence principle, presentation by Bohr of      II163
Coster screening doublet terms and Coster relativsitic doublet terms      II205
Covalent bond, Heitler and Longons Quantum mechanical elucidation of      III223
Covalent bond, Lewis and Langmuirs phenomenological introduciton of      II198
Crowther $\delta$-function Diracs      III175
Crowther single and multiple scatterings of $\beta$-rays      1207 219
Darwin attempt to introduce spin of vector type      III214
Darwin on Dirac electron equation and fine structure constant      III232
Darwin theory of scattering and absorption of $\alpha$-particles      1222
Davisson Kunsman      II261
de Broglie prediction of diffraction of electrons      II251
de Broglie supposition of small mass for light quantum      II248
de Broglie virtual wave (phase wave) and the quantum condition      II249
de Broglie waves theory of gases and flactuation in gases in terms of      II259 III72
de Broglie Andrade e Silva $\nu$-wave and light      III297
de Hass      II190
Debye derivation of Planks distribution formula      1118 261
Debye hypothesis of elementary action and unharmonic oscillators      II114
Debye theory of Compton effect      II239
Debye theory of specific heats of solids      1123
Debye Zeeman effect and the quantum condition      II141
Dennison, determination of nuclear spin of hydrogen atom      III223
Difficulty of frequency in classical oscillation models of spectral series      173
Difficulty of frequency in wave equation      III78
Dirac commutation relation and Poisson bracket equation      III46
Dirac difficulty in matrix mechanics for many-body systems      III147
Dirac equation of motion in $q$-numbers      III47
Dirac introduction of $\delta$-function      III 175
Dirac introduction of transformation functions      III176
Dirac matrices with continuous row and/or column      III174
Dirac number representation of wave equation      III209
Dirac permutation symmetry of $\psi$ for a many-body system      III148
Dirac quantization of radiation as a system of light quanta      III210
Dirac relativitization of matrix mechanics      III204
Dirac relativitization of wave equation      III150 154
Dirac spin-orbit interaction based on Diracs electron equation      III232
Dirac theory of positive electron      III234
Dirac transformation function and Borns scattering probability      III182
Dirac transition probability of absorption and induced emission of radiation      III158
Dirac treatment of Balmer formula by Dirac $q$-numbers      III42
Dirac treatment of equation of electron orbit by $q$-numbers      III51
Dirac wave equation (time-dependent)      III154 181
Dirac Compton effect by matrix mechanics      III204
Discussion of number of inneratoic electrons      0182 186 190 193
Dispersion formula and Heisenbergs quantum ondition      III11 14
Dispersion formula by wave mechanics (Schr$\ddot{o}$dinger)      III118
Dispersion formula, Borns      II277
Dispersion formula, Kramers      II273
Dispersion formula, Kramers Heisenbergs      II282 III6
Dispersion formula, Ladenberg Reiches      II272
Displacement law of spectral series      II180
Displacement law, Wiens      18 118
Distribution law of black body radiation, Michelsons      113 117
Distribution law, Plancks      125 1111
Distribution law, Rayleigh Jeans      122 1112
Distribution law, Wiens      116 118
Doubleness of the electron Indication of (Pauli)      II215
Drude determination of inneratomic electrons (by method of light dispersion)      1191 1120
Dual nature of radiation, indication by Einstein of      1132
Dual nature of radiation, intermediary viewpoint of      II160 241
Dual nature of radiation, solution of conflict in      III206
Duane      see Clark Dynamiden
Duane light quantum and Bragg reflection      II241
Duane number in a hydrogen atom of      0165
Duane their true radius and specific absorption power of cathode rays      1166
Duane Lenards model of atom by      0163
Ehrenfest      see Epstein-
Ehrenfest adiabatic hypothesis      II164
Ehrenfest adiabatic hypothesis and the quantum condition      II165
Ehrenfest hypothesis of elementary action and rotational motion      II115
Ehrenfest Kamerlingh Onnes analysis of number of complexion      II257
Einstein demand for a quantum-theoretical theory of radiation      II156
Einstein derivation of Plancks distribution formula      II150 258
Einstein fluctuation in a gas and de Broglie waves      II259
Einstein fluctuation of radiation energy      1127
Einstein fluctuation of radiation pressure      1131
Einstein hypothesis of light quantum      143
Einstein indication of contradictions in theory of radiation      117
Einstein indication of dual nature of radiation      II32
Einstein indication of existence of adiabatic invariants      II165
Einstein introduction of transition probability      II149
Einstein out-radiation, positive and negative in-radiation      II149
Einstein quantum-statistical mechanics of ideal gases      II255
Einstein recoil of molecule in the theory of light quantum      II151
Einstein relation between the elementary action and $e^{2}/c$      II42
Einstein theory of specific heats of solids      II19 22
Einstein Ehrenfest difficulty in interpretation of Stern Gerlachs experiment      II193
Einstein Podolsky Rosen      see EPR Electrion
Einstein Podolsky Rosen, Kelvins model of atoms without nucleus using      0115
Einstein Podolsky Rosen, Kelvins name for electron      1116
Electromagnetic field equations Attempt to matrixize      III33
Electron configuration by Bohr      II98 202
Electron configuration by Kossel      II196
Electron configuration by Stoner      II211
Electron configuration of rare gas atoms (Rydberg)      II198
Electron configuration, conjugate      II217
Electron diffraction, Elsassers Indication of experimental evidence for      II260
Electron diffraction, prediction by de Broglie of      II251
Electron specific charge, magnetomechanical anomaly of      II190 213
Electron specific charge, Thomsons Measurement on free electrons of      01II
Electron specific charge, Zeemans measurement using the Zeeman effect      092
Elementary action and radius of atom of Nagaoka type      72 73
Elementary action and radius of atom of Thomson type      144
Elementary action, relation to $e^{2}/c$ (Einstein)      II42
Elementary electric charge, equality of positive and negative elementary charges      1114
Elementary electric charge, measurement by Thomson of (by gas ionization method)      1111
Elementary electric charge, measurement by Townsend of (by ion diffusion method)      1113
Elementary electric charge, measurement by Wilson of (by falling drop method)      1113
Elester Geiter      178
Elsasser indication of experimental evidence of wave nature of electron      II260
Energy quantum (element) of resonator      131
Entropy of Plancks resonator      119 25 30 15
Entropy of the radiation obeying Wien distribution law      041
EPR      see Einstein Podolsky Rosen EPRs question
EPR on interpretation of quantum EPR, Einstein Podolsky Rosen EPRs question, mechanics      III279 282 299
EPR, Bohrs and Furrys replies to      III282 285
EPR, problem of      III280 282
Epstein equality of Sommerfelds and Plancks quantum conditions      II140
Epstein wuantum condition and Stark effect      II132
Epstein Ehrenfest light quantum and X-ray diffraction      II244
Equation of motion in $q$-number (Dirac)      III47
Equation of motion in matrix mechanics (Born Jordan)      III25
Equipartition law of energy and Rayleigh Jeans distribution formula      137 1112
Eucken      II115
Example of cat, Schr$\ddot{o}$dinger critique of v. Neumanns theory of observation      III268
Exclusion principle, presentation by the name of general rule      II207 218
Fermat principle and Hamilton principle      II240 III80
Fermi quantization of ideal gas      III153
Fermi Dirac statistics      II260 III153
Field quantization, beginning of (Born Heisenberg Jordan)      III37
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