Quantum Mechanics

In General > s.a. formulations; foundations [including ontology]; interpretations; logic; quantum systems.
* Regime: Situations where length scales are small wrt energy scales, and a small number of states are occupied.
* Features: Formally, the most important concept introduced with respect to classical mechanics is that of probability amplitudes, with their particular combination laws; These yield amplitudes for processes, described in terms of unique (classical) trajectories; Physically, the corresponding distinguishing features are complementarity and entanglement.
> Features: see complementarity; entanglement; uncertainty; Wave-Particle Duality.
> Related topics: see experiments; measurement; modified versions; particle effects; semiclassical.

General Concepts and Aspects > s.a. diffraction [Kapitza-Dirac]; effects; probability; quantum states; waves.
* Probability current: Can be constructed from the wave function by j:= # Im(* ); The integral lines for this current are analogous to trajectories; > s.a. path integrals.
@ General references: Houston AJP(37); Gudder & Boyce IJTP(70); Jauch in(71); Komar in(71); Giles in(75); Loinger RNC(87); Amann et al ed-88; Drieschner et al IJTP(88); Von Baeyer ThSc(91); Foschini qp/98 [logical structure]; Bub SHPMP(00)qp/99; Arndt et al qp/05-in, comm Mohrhoff qp/05; Nikolic qp/06 [myths and facts]; Rieffel qp/07-in [from information pov].
@ Geometric aspects: Komar GRG(76); Geroch ln; Kibble CMP(79); Bernard & Choquet-Bruhat 88; Rzewuski RPMP(88); Cirelli et al JMP(90), JMP(90); Collas PLA(90); Dubrovin et al MPLA(90) [Kähler structures]; Anandan FP(91); Dimakis & Müller-Hoissen JPA(92) [non-commutative symplectic geometry]; Schilling PhD(96); Ashtekar & Schilling gq/97; Isidro JPA(02)qp/01; Klauder qp/01 [metric on phase space]; Cariñena et al a0707-in [and quantum-classical transition]; Varadarajan 07; > s.a. formulations of quantum mechanics, geometric quantization.
> Related topics: see angular momentum; complex structure; euclidean geometry; information; lie algebra; mind; Momentum; observables; Phase; schrödinger; spacetime; Supersymmetry; Trajectories.

References > s.a. history of quantum mechanics; logic; physics teaching; symmetries.
@ Original papers: Heisenberg ZP(25); Born & Jordan ZP(25); Born et al ZP(26); Dirac PRS(26); Van der Waerden ed-67.
@ Texts: Bohm 51; Dirac 58; Dicke & Wittke 60; Fermi 61; Messiah 62; Blokhintsev 64; Dirac 64; Kramers 64; Gottfried 66; Fluegge 75; Martin 81; Prigovecki 81; Sokolov, Ternov & Zhukovskii 84; Pauling & Wilson 85; Sakurai 85; Das & Melissinos 86; Wu 86; Schwabl 88; Umezawa & Vitiello; Fayyazuddin & Riazuddin 90; Galindo & Pascual 90; Greenhow 90; Lévy-Leblond & Balibar 90; Van Fraassen 91; Park 92; Peebles 92; A Bohm 93; Thankappan 93; Greiner 94; McGervey 95; Gottfried & Yan 03; Liboff 03; Ghatak & Lokanathan 04; Basdevant & Dalibard 05; Müller-Kirsten 06 [especially path integral]; Basdevant 07.
@ Texts, conceptual: Jauch 68; Mayants 84; Krips 88; d'Espagnat 89, 95; Ballentine 90, 98; Peres 94; Bitbol 96; Home 97.
@ Texts, with computers: Brandt & Dahmen 94, 95, 97; McMurry 94; Steeb 94 [REDUCE]; Thaller 04 [animations].
@ Texts, problems: ter Haar ed-75; Squires 95; Lim 98; Capri 02; Tamvakis 05; Basdevant & Dalibard 06.
@ Texts, applications: Singh 97; Landshoff et al 98; Fitts 99 [chemistry]; Harrison 00; Robinett 06 [II]; Swanson 06.
@ I: Hoffmann 59; Bohr 61; Bergmann 62; Guillemin 68; Hey & Walters 87; Rohrlich 87; Albert 93; Gilmore 94; Zukav 94; Styer 00; Al-Khalili 03; Bruce 04.
@ II: Eisberg & Resnick 74; Sudbery 86 [particle physics]; Chester 87; Smith 91 [historical]; Bialynicki-Birula et al 92; Townsend 92; McMurry 94; Griffiths 95; Omnès 99 [conceptual]; Levin 01; Capri 02; Rae 02; Gasiorowicz 03; Englert 06 [II/III].
@ III: Dyson 51 & qp/06 [advanced]; Schiff 68; Lipkin 73 [selected topics]; Cohen-Tannoudji et al 77; Shankar 94; Merzbacher 98; Rosu phy/98-ln; Lindenbaum 99; Schwabl 05 [advanced]; Cohen qp/06-ln [II/III]; Dyson & Derbes 07; Gyftopoulos a0709 [current understanding].
@ III, operational / qualitative: Migdal 77; Busch et al 95.
@ III, mathematical: Von Neumann 55; Mackey 63; Nikodym 66; Hannabuss 97 [coherent states, group reps]; Kalmbach 98; Steeb 98; Naudts mp/00 [from symmetry]; Komech mp/05-ln; Villaseñor a0804-in [Segal's approach].
@ Applications: Aspelmeyer & Zeilinger pw(08)jul.
@ And foundations of physics: Benioff PRA(99)qp/98; Neumaier qp/00; > s.a. foundations of quantum mechanics.
@ Abstract: Mielnik CMP(68); Piron 76; Ludwig 83-85, 85-87.
@ And group theory: Weyl 50; Mackey 68; Simms 68; Aldaya & Azcárraga FdP(87); Mirman 95.

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