Types of Quantum States  

In General > s.a. [quantum states]; entanglement; locality; mixed states; pilot wave ["non-quantum"]; schrödinger equation.
$ Pure states: A state s is pure if there are no two distinct states s1 and s2 and positive c1 and c2 such that s = c1s1 + c2s2.
$ Separable states: If A and B are two subsystems, separable states are the non-entangled ones, of the form

= k k Ak  Bk ,      where      k k = 1 .

* Unstable/decaying states: Can be associated with resonances, and described by a Rigged Hilbert space.
* Schrödinger cat states: Superpositions of well-separated coherent states.
@ Separable states: Peres PRL(96)qp [necessary condition]; Sanpera et al qp/97 [characterization]; Zyczkowski et al PRA(98) [volume]; Majewski OSID(99)qp/97 [rigorous description]; Lockhart et al QIC(02)qp/00 [product states]; Shi & Du qp/01 [boundary]; Wu & Anandan PLA(02), Rudolph PLA(04) [criteria]; Albeverio et al PRA(03)qp [reduction criterion]; Wu PLA(04) [as convex sum]; Timpson & Brown IJQI(05)qp/04 [proper vs improper]; Raggio qp/05 [spectral conditions]; Khasin et al qp/07 [negativity as measure of non-separability].
@ Energy eigenstates: Halliwell & Thorwart PRD(02)gq [and dynamics]; Moriconi AJP(07)qp [number of nodes].
@ Ground state: Mouchet JPA(05)qp/04 [energy estimation method].
@ Bound states: Chadan et al JMP(96) [bound on number]; Chadan & Kobayashi JMP(97) [sufficient condition]; Aktosun et al JMP(98) [number, 1D]; Chadan et al JMP(99) [number]; Brau & Calogero JPA(03)mp/04, Brau JPA(03)mp/04, JPA(04)mp [central V, conditions and bounds]; Chadan et al JMP(03) [number, 1D and 2D]; Ritchie PLA(06) [relativistic]; > s.a. atomic, oscillator, systems.
@ Unstable states: Ordonez et al PRA(01) [dressed]; Chruscinski mp/02 [Wigner functions for damped systems]; Castagnino et al PLA(01)qp/02; Kielanowski qp/03-in; > s.a. resonance.
@ Metastable states: Davies JFA(82) [dynamical stability].
@ Bipartite states: Yu et al RPMP(07)-a0711 [differential geometry]; > s.a. entanglement.
@ In atoms: Bialynicka-Birula & Bialynicki-Birula PRA(97) + pn(97)nov [Trojan states]; Calsamiglia et al PRL(01)cm [macroscopic superpositions].
@ Other states: Mould FPL(01)qp, qp/01, Ferrero et al FP(04) [physical vs subjective]; in Sanz JPA(05)qp/04 [nowhere differentiable]; Jeong & Ralph qp/05-in [Schrödinger cat states, application]; de Oliveira et al PhyA(05), Malbouisson et al PhyA(07) [displaced number states]; Luís PRA(07) [exponential, using Rényi entropy as uncertainty measure].

Semiclassical States > s.a. constrained systems; quantum field theory states; semiclassial quantum mechanics; wigner functions.
* Idea: States with a classical interpretation, in which the probability distributions for a chosen set of observables are narrowly peaked around classical values; Common examples are coherent and squeezed states.
$ Def: A set of semiclassical states is a collection {|} of states labelled by points in in phase space, together with a set {(Fi, i, i)} of observables and tolerances, such that ||Fi| – Fi( )| i and (Fi)omega2 i, for all and i.
@ Minimum uncertainty: Trifonov et al PRL(01) [discrete-valued observables]; Detournay et al PRD(02) [with gup]; de Gosson PLA(04) [optimal]; > s.a. coherent, Squeezed States.
@ With classical behavior: Davidovic & Lalovic JPA(98); > s.a. semiclassical quantum mechanics.
@ Constrained systems: Shvedov ht/01 [first-class], mp/05-in [linear C, quadratic H]; Ashtekar et al PRD(05)gq [kinematical and physical states].
@ Special systems: Arsenovic et al PRA(99) [for spin-1/2]; Blanchard & Olkiewicz PLA(00) [open systems]; Yang & Kellman PRA(02) [EBK wave function near resonance]; Dell'Antonio & Tenuta JPA(04)mp/03 [with constraining potential]; Schulman PRL(04) [particles, evolution of spreads]; > s.a. photon, semiclassical quantum gravity [including non-classical].
@ Other topics: de Gosson mp/02 [symplectic area]; Solovej & Spitzer CMP(03) [semiclassical calculus]; Genoni et al PRA(07)-a0704 [departure from Gaussianity].

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