Q nt C n pt n h An Alt rn t v Appr h t th Und r t nd n f Q nt M h n
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MA CO M O GAI C v nd h b r t r , Un v r t f C br d
CAM I GE U I E SI Y ESS Preface page xii Acknowledgements xvi
rt h v r f Q nt
h nd th r t l ph n 8 . h tr ph f n n t nth nt r ph .2 At nd l l n th n n t nth nt r 4 . h n t th r f nd ltz nn t t t l h n 6 .4 M x ll t n f r th l tr n t f ld . h M h l n—M rl xp r nt nd th th r f r l t v t .6 h r n f p tr l l n . h p tr f bl b d r d t n .8 h th r n t r 2
2 l n nd bl b d r d t n 24 2. h r l f xp r nt l t hn 24 2.2 8 00: h h n n l nd p f xp r nt l ph 2 2. l n nd th p tr f bl b d r d t n 2 2.4 rd th p tr f bl b d r d t n 6 2. C p r n f th l f r bl b d r d t n th xp r nt 4 2.6 l n th r f bl b d r d t n 42 2. l n nd n t r l n t 4 2.8 l n nd th ph l n f n f h 46
E n t n nd nt 00 48 . E n t n n 0 48 .2 E n t n n r n n t n 4 . On a heuristic viewpoint concerning the production and transförmation of light (E n t n 0 0 .4 h nt th r f l d . b th r f p f h t 8 .6 l t t n f p rt l nd v — E n t n ( 0 60 . h r t S lv C nf r n 64 .8 h nd f th b nn n 6 v v C nt nt
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4 h hr d l f th h dr n t 4. h n ff t: r ntz nd r r nt rpr t t n 4.2 h pr bl f b ld n d l f t 4 4. h n nd th rf rd 4.4 nd h l n d l f t 4. h hr d l f th h dr n t 80 4.6 M l nd th r p tr f th h l l nt 8 4. h r n rtz xp r nt 88 4.8 h r pt n f hr th r f th t 8
S rf ld nd Ehr nf t n r l n th hr d l 0 . Intr d t n 0 .2 S rf ld xt n n f th hr d l t ll pt l rb t . S rf ld nd th f n tr t r n t nt 6 .4 A th t l nt rl d fr t n t lt n b . S rf ld d l f th t n thr d n n 0 .6 Ehr nf t nd th d b t pr n pl . h d v l p n nfr tr t r f nt th r 8
6 E n t n ff nt , hr rr p nd n pr n pl nd th f r t l t n r l 6. h pr bl f tr n t n b t n t t n r t t 6.2 On the quantum theory of radiation (E n t n 6 20 6. hr rr p nd n pr n pl 2 6.4 h f r t l t n r l 2 6. h p l r t n f nt d r d t n nd l t n r l 2 6.6 h db r r nd th nt d f t 2 6. rd r pl t nt th r f t
Und r t nd n t p tr dd t n l nt n b r . Opt l p tr p , lt pl t nd th pl tt n f p tr l l n .2 h St r ff t 8 . h n ff t 42 .4 h n l n ff t 4 . h rn tt, E n t n d nd St rn G rl h xp r nt
8 hr d l f th p r d t bl nd th r n f p n 8. hr f r t d l f th p r d t bl 8.2 h W lf hl l t r nd hr nd th r f th p r d t bl 8. r l v l nd St n r r v d p r d t bl 64 8.4 l x l n pr n pl 68 8. h p n f th l tr n 6 x Contents
h v — p rt l d l t 172 9.1 The Compton effect 172 9.2 Bose—Einstein statistics 174 9.3 De Broglie waves 177 9.4 Electron diffraction 181 9.5 What had been achieved by the end of 1924 183
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0 h ll p f th ld nt th r nd th d f t r n r t n 189 10.1 Ladenburg, Kramers and the theory of dispersion 189 10.2 Slater and the Bohr—Kramers—Slater theory 194 10.3 Born and `quantum mechanics' 197 10.4 Mathematics and physics in Göttingen 200
h nb r br thr h 203 11.1 Heisenberg in Göttingen, Copenhagen and Helgoland 203
11.2 Quantum theoretical re interpretation of kinematic and mechanical relations (Heisenberg, 1925) 205 11.3 The radiation problem and the translation from classical to quantum physics 207 11.4 The new dynamics 212 11.5 The nonlinear oscillator 214 11.6 The simple rotator 221 11.7 Reflections 222
2 M tr x h n 224 12.1 Born's reaction 224 12.2 Born and Jordan's matrix mechanics 226 12.3 Born, Heisenberg and Jordan (1926) — the Three-Man Paper 232 12.4 Pauli's theory of the hydrogen atom 241 12.5 The triumph of matrix mechanics and its incompleteness 245
r nt h n 247 13.1 Dirac's approach to quantum mechanics 247 13.2 Dirac and The fundamental equations of quantum mechanics (1925) 248
13.3 Quantum algebra, q and c-numbers and the hydrogen atom 255 13.4 Multi-electron atoms, On quantum algebra and a PhD dissertation 259
4 S hröd n r nd v h n 261 14.1 Schrödinger's background in physics and mathematics 261 14.2 Einstein, De Broglie and Schrödinger 263 14.3 The relativistic Schrödinger wave equation 267 14.4 Quantisation as an Eigenvalue Problem (Part I) 269 x Contents
14.5 Quantisation as an eigenvalue problem (Part 2) 274 14.6 Wave-packets 281 14.7 Quantisation as an eigenvalue problem (Part 3) 284 14.8 Quantisation as an eigenvalue problem (Part 4) 289 14.9 Reflections 291
n l n tr x nd v h n 292 15.1 Schrödinger (1926d) 293 15.2 Lanczos (1926) 298 15.3 Born and Wiener's operator formalism 299 15.4 Pauli's letter to Jordan 302 15.5 Eckart and the operator calculus 304 15.6 Reconciling quantum mechanics and Bohr's quantisation of angular momentum - the WKB approximation 307 15.7 Reflections 310
6 Sp n nd nt t t t 312 16.1 Spin and the Lande g-factor 312 16.2 Heisenberg and the helium atom 315 16.3 Fermi-Dirac statistics - the Fermi approach 318 16.4 Fermi-Dirac statistics - the Dirac approach 320 16.5 Building spin into quantum mechanics - Pauli spin matrices 324 16.6 The Dirac equation and the theory of the electron 327 16.7 The discovery of the positron 338
h nt rpr t t n f nt h n 343 17.1 Schrödinger's interpretation (1926) 343 17.2 Born's probabilistic interpretation of the wavefunction e (1926) 345 17.3 Dirac-Jordan transformation theory 349 17.4 The mathematical completion of quantum mechanics 355 17.5 Heisenberg's uncertainty principle 357 17.6 Ehrenfest's theorem 360 17.7 The Copenhagen interpretation of quantum mechanics 362
8 h ft r th 368 18.1 The development of theory 368 18.2 The theory of quantum tunnel ling 372 18.3 The splitting of the atom and the Cockcroft and Walton experiment 375 18.4 Discovery of the neutron 377 18.5 Discovery of nuclear fission 378 18.6 Pauli, the neutrino and Fermi's theory of weak interactions 379 18.7 Cosmic rays and the discovery of elementary particles 381 18.8 Astrophysical applications 383 x C nt nt
Epilogue 88 Notes 8 References 40 Name index 4 2 Subject index 4 6