Quantum Mechanics: A Modern Development
Abstract
Although there are many textbooks that deal with the formal apparatus of quantum mechanics (QM) and its application to standard problems, none take into account the developments in the foundations of the subject which have taken place in the last few decades. There are specialized treatises on various aspects of the foundations of QM, but none that integrate those topics with the standard material. This book aims to remove that unfortunate dichotomy, which has divorced the practical aspects of the subject from the interpretation and broader implications of the theory.The book is intended primarily as a graduate level textbook, but it will also be of interest to physicists and philosophers who study the foundations of QM. Parts of it could be used by senior undergraduates too.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
To ensure compatibility of non-relativistic quantum mechanics with the equivalence principle, one generally invokes a superselection rule that prevents a quantum particle from being found in superposition states of different masses.
“To ensure the compatibility of non-relativistic quantum mechanics with EP, one generally invokes a superselection rule [15], originally proposed by Bargmann [16], which prevents a quantum particle from being found in superposition states of different masses.”
From Equivalence principle and quantum mechanics: quantum simulation with entangled photons (2018) · cites this paper as [15]
Bargmann's superselection rule Δm = m2 - m1 = 0 is a necessary requirement to avoid equivalence principle violation.
“Bargmann's superselection rule ∆ m = m 2 -m 1 = 0 is thus viewed as a necessary requirement to avoid EP violation [15, 16].”
From Equivalence principle and quantum mechanics: quantum simulation with entangled photons (2018) · cites this paper as [15]
Cited by
Sorted by citations
Robinett, R. W. (2004) · Physics Reports · doi:10.1016/j.physrep.2003.11.002 · Cited by 526 · see citing works
“[119] for a similar result for the case when pA = pB = 0; see also Ref.”
BackgroundOpen Quantum Systems. An Introduction
Rivas, Á., & Huelga, S. F. (2011) · arXiv · doi:10.48550/arxiv.1104.5242 · Cited by 424 · see citing works
Classical and Quantum Fluctuation Theorems for Heat Exchange
Jarzynski, C., & Wojcik, D. K. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.230602 · Cited by 362 · see citing works
“where H is the system Hamiltonian, and Θ is the quantum time-reversal operator [17, 18].”
BackgroundTeaching quantum mechanics on an introductory level
Müller, R., & Wiesner, H. (2002) · American Journal of Physics · doi:10.1119/1.1435346 · Cited by 291 · see citing works
Numerical study of the topological Anderson insulator in HgTe/CdTe quantum wells
Jiang, H. W., Wang, L., Sun, Q., & Xie, X. (2009) · Physical Review B · doi:10.1103/physrevb.80.165316 · Cited by 279 · see citing works
Erhart, J., Sponar, S., Sulyok, G., Badurek, G., Ozawa, M., & Hasegawa, Y. (2012) · Nature Physics · doi:10.1038/nphys2194 · Cited by 258 · see citing works
Recent advances in Wigner function approaches
Weinbub, J., & Ferry, D. K. (2018) · Applied Physics Reviews · doi:10.1063/1.5046663 · Cited by 248 · see citing works
Delayed-choice gedanken experiments and their realizations
Ma, X., Kofler, J., & Zeilinger, A. (2016) · Reviews of Modern Physics · doi:10.1103/revmodphys.88.015005 · Cited by 222 · see citing works
“Note that similar setups were proposed by Grangier (1986), Ballentine (1998), and Kwiat and Englert (2004).”
MethodA classification of entanglement in three-qubit systems
Sabín, C., & Alcaine, G. G. (2008) · The European Physical Journal D · doi:10.1140/epjd/e2008-00112-5 · Cited by 217 · see citing works
“∗Electronic address: csl@imaff.cfmac.csic.es †Electronic address: ggarciaa@fis.ucm.es 2”
Massively parallel quantum computer simulator
Raedt, K. D., Michielsen, K. F. L., Raedt, H. A. D., Trieu, B., Arnold, G., Richter, M., Lippert, T., Watanabe, H., & Ito, N. (2006) · Computer Physics Communications · doi:10.1016/j.cpc.2006.08.007 · Cited by 213 · see citing works
“The frequency of obtaining 0 (1) can be estimated by repeated measurement of the same state of the qubit and is given by | a 0 | 2 ( | a 1 | 2 ) [9–11].”
BackgroundEssential entanglement for atomic and molecular physics
Tichy, M. C., Mintert, F., & Buchleitner, A. (2011) · Journal of Physics B Atomic Molecular and Optical Physics · doi:10.1088/0953-4075/44/19/192001 · Cited by 220 · see citing works
sl(2, ) as a complex Lie algebra and the associated non-Hermitian Hamiltonians with real eigenvalues
Bagchi, B. K., & Quesne, C. (2000) · Physics Letters A · doi:10.1016/s0375-9601(00)00512-0 · Cited by 192 · see citing works
“into the underpinnings of the theory [ 1 ], on the other, group theoretical methods have”
BackgroundRecent developments in photon-level operations on travelling light fields
Kim, M. S. (2008) · Journal of Physics B Atomic Molecular and Optical Physics · doi:10.1088/0953-4075/41/13/133001 · Cited by 212 · see citing works
Trinity of relational quantum dynamics
Höhn, P. A., Smith, A. R. H., & Lock, M. P. E. (2021) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.104.066001 · Cited by 189 · see citing works
Is there something quantum-like about the human mental lexicon?
Bruza, P., Kitto, K., Nelson, D. L., & McEvoy, C. L. (2009) · Journal of Mathematical Psychology · doi:10.1016/j.jmp.2009.04.004 · Cited by 171 · see citing works
“which has an unbounded continuous spectrum corresponding to the idea that space is a continuum and that each of the three position measurements commute (4).”
InfluentialRideout, D., Jennewein, T., Giovanni Amelino-camelia, A., Demarie, T. F., Higgins, B. L., Kempf, A., Kent, A., Laflamme, R., Ma, X., Mann, R. B., et al. (2012) · Classical and Quantum Gravity · doi:10.1088/0264-9381/29/22/224011 · Cited by 168 · see citing works
“lead to problems when relativity is considered, in particular with situations in which spacelike separated measurements take place [20, 21]. Other interpretations, such as the ensemble interpretation [27] or consistent histories [28] will be perfectly compatible with the expected outcomes of these experiments [29]. Sp…”
ResultMany-body density matrices for free fermions
Cheong, S. A., & Henley, C. L. (2004) · Physical Review B · doi:10.1103/physrevb.69.075111 · Cited by 164 · see citing works
Nikolić, B. K., Zârbo, L. P., & Souma, S. (2006) · Physical Review B · doi:10.1103/physrevb.73.075303 · Cited by 153 · see citing works
Modeling electromagnetic resonators using quasinormal modes
Kristensen, P. T., Herrmann, K., Intravaia, F., & Busch, K. (2020) · Advances in Optics and Photonics · doi:10.1364/aop.377940 · Cited by 167 · see citing works
Handbook of Relativistic Quantum Chemistry
Liu, W. (2016) · Springer eBooks · doi:10.1007/978-3-642-40766-6 · Cited by 156 · see citing works
Recent developments in photon-level operations on travelling light fields
Kim, M. (2008) · Research Portal (Queen's University Belfast) · Cited by 144 · see citing works
Quantum teleportation and Bell’s inequality using single-particle entanglement
Lee, H.-W., & Kim, J. (2000) · Physical Review A · doi:10.1103/physreva.63.012305 · Cited by 138 · see citing works
Nikolić, B. K., & Souma, S. (2005) · Physical Review B · doi:10.1103/physrevb.71.195328 · Cited by 134 · see citing works
Beisbart, C., & Hartmann, S. (2011) · doi:10.1093/acprof:oso/9780199577439.001.0001 · Cited by 134 · see citing works
Extrinsic Spin Hall Effect Induced by Resonant Skew Scattering in Graphene
Ferreira, A., Rappoport, T. G., Cazalilla, M. A., et al. (2014) · Physical Review Letters · doi:10.1103/physrevlett.112.066601 · Cited by 127 · see citing works
Belloni, M., & Robinett, R. W. (2014) · Physics Reports · doi:10.1016/j.physrep.2014.02.005 · Cited by 127 · see citing works
Quantum oscillations and black hole ringing
Frederik Denef, B., Hartnoll, S. A., & Subir Sachdev, A. (2009) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.80.126016 · Cited by 139 · see citing works
Quantum states for primitive ontologists
Belot, G. (2012) · European Journal for Philosophy of Science · doi:10.1007/s13194-011-0024-8 · Cited by 89 · see citing works
Quantum erasure with causally disconnected choice
Ma, X., Kofler, J., Qarry, A., Tetik, N., Scheidl, T., Ursin, R., Ramelow, S., Herbst, T., Ratschbacher, L., Fedrizzi, A., et al. (2013) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1213201110 · Cited by 118 · see citing works
Master equations and the theory of stochastic path integrals
Weber, M. F., & Frey, E. (2017) · Reports on Progress in Physics · doi:10.1088/1361-6633/aa5ae2 · Cited by 110 · see citing works
A modal-Hamiltonian interpretation of quantum mechanics
Lombardi, O., & Castagnino, M. (2008) · Studies in History and Philosophy of Science Part B Studies in History and Philosophy of Modern Physics · doi:10.1016/j.shpsb.2008.01.003 · Cited by 109 · see citing works
“When we say that [ ]A,B iC= ( 0C ≠ ) and, therefore, 1 2A B / C∆ ∆ ≥ (see Ballentine, 1998, pp. 223-224), both A∆ and B∆ can be computed in terms of the respective expectation values A ρ and B ρ in the quantum ensemble.”
BackgroundMethodInfluentialScalar quantum kinetic theory for spin-1/2 particles: mean field theory
Zamanian, J., Marklund, M., & Brodin, G. (2010) · New Journal of Physics · doi:10.1088/1367-2630/12/4/043019 · Cited by 108 · see citing works
“Bohm, and others to give a close-to classical interpretation of the Schrödinger equation by Hamilton-Jacobi theory shows that, if one is inclined to stick to this interpretational scheme and extend this to statistical interpretations, one has to consider the wave function rather as an ensemble of (nonclassical [43, 44…”
BackgroundVeitch, V., Wiebe, N., Ferrie, C., & Emerson, J. (2013) · New Journal of Physics · doi:10.1088/1367-2630/15/1/013037 · Cited by 107 · see citing works
Particle diffraction studied using quantum trajectories
Sanz, Á. S., Borondo, F., & Miret-Artés, S. (2002) · Journal of Physics Condensed Matter · doi:10.1088/0953-8984/14/24/312 · Cited by 105 · see citing works
Atom–surface diffraction: a trajectory description
Guantes, R., Sanz, Á. S., Margalef-Roig, J., & Miret-Artés, S. (2004) · Surface Science Reports · doi:10.1016/j.surfrep.2004.02.001 · Cited by 100 · see citing works
“The existence of wavy properties associated to material particles is one of the fundamental achievements of quantum mechanics [152].”
BackgroundRideout, D., Jennewein, T. D., Giovanni Amelino-camelia, A., Demarie, T. F., Higgins, B. L., Kempf, A., Kent, A., Laflamme, R., Ma, X., (3413621), R. M., et al. (2016) · Cited by 118 · see citing works
Three-nucleon forces: implementation and applications to atomic nuclei and dense matter
Hebeler, K. (2020) · TUbilio (Technical University of Darmstadt) · Cited by 101 · see citing works
Pearle, P. (2009) · The Western Ontario series in philosophy of science · doi:10.1007/978-1-4020-9107-0_14 · Cited by 94 · see citing works
Universality of the negativity in the Lipkin-Meshkov-Glick model
Wichterich, H. C., Vidal, J., & Bose, S. (2010) · Physical Review A · doi:10.1103/physreva.81.032311 · Cited by 91 · see citing works
Impurities as a quantum thermometer for a Bose-Einstein condensate
Sabín, C., White, A., Hackermüller, L., et al. (2014) · Scientific Reports · doi:10.1038/srep06436 · Cited by 89 · see citing works
“Therefore, to ensure that there are no transitions between the U(θ) |n±〉 states, we make use of the adiabatic approximation [44] ∑ m |〈m|Ḣ|n〉| Em−En t << 1.”
Decompositions of general quantum gatesPreprint
Möttönen, M., & Vartiainen, J. J. (2005) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0504100 · Cited by 87 · see citing works
“1 Introduction The emerging of quantum mechanics [1] in the beginning of the 20th century revolutionized the field of physics bringing not only understanding to fundamental concepts such as atomic and particle physics, but also numerous applications for everyday life.”
BackgroundVarga, I., & Pipek, J. (2003) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.68.026202 · Cited by 84 · see citing works
Conservation and entanglement of Hermite-Gaussian modes in parametric down-conversion
Walborn, S. P., Pádua, S., & Monken, C. H. (2005) · Physical Review A · doi:10.1103/physreva.71.053812 · Cited by 83 · see citing works
Autonomous quantum thermodynamic machines
Tonner, F., & Mahler, G. (2005) · Physical Review E · doi:10.1103/physreve.72.066118 · Cited by 84 · see citing works
Relativistic quantum effects of confining potentials on the Klein-Gordon oscillator
Vitória, R. L. L., & Bakke, K. (2016) · The European Physical Journal Plus · doi:10.1140/epjp/i2016-16036-4 · Cited by 83 · see citing works
Benchmarking gate-based quantum computers
Michielsen, K., Nocon, M., Willsch, D., Jin, F., Lippert, T., & De Raedt, H. (2017) · Computer Physics Communications · doi:10.1016/j.cpc.2017.06.011 · Cited by 82 · see citing works
“If quantum theory is assumed to describe the operation of the device, each measurement constitutes a statistically independent trial [10].”
BackgroundInfluentialCombinatorics and Boson normal ordering: A gentle introduction
Błasiak, P., Horzela, A., Penson, K. A., Solomon, A. I., & Duchamp, G. (2007) · American Journal of Physics · doi:10.1119/1.2723799 · Cited by 86 · see citing works
Non-Markovian dynamics of a damped driven two-state system
Haikka, P., & Maniscalco, S. (2010) · Physical Review A · doi:10.1103/physreva.81.052103 · Cited by 77 · see citing works
Finally making sense of the double-slit experiment
Aharonov, Y., Cohen, E., Colombo, F., Landsberger, T., Sabadini, I., Struppa, D. C., & Tollaksen, J. (2017) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1704649114 · Cited by 74 · see citing works
“From our perspective, and consistent with ideas first expressed by Born [6] and thereafter extensively developed by Ballentine [7, 8], a wavefunction represents an ensemble property as opposed to a property of an individual system.”
MethodSelf-induced decoherence: a new approach
Castagnino, M., & Lombardi, O. (2003) · Studies in History and Philosophy of Science Part B Studies in History and Philosophy of Modern Physics · doi:10.1016/j.shpsb.2003.03.001 · Cited by 74 · see citing works
“…of continuous or quasi-continuous nature introduce the continuous part of the spectrum and make the off-diagonal terms of the reduced density operator vanish; this is the case of the spin recombination experiment which takes place in a single crystal interferometer (see Ballentine, 1998).”
BackgroundBayesian Probability Theory: Applications in the Physical Sciences
von der Linden, W., Dose, V., & von Toussaint, U. (2014) · Cited by 74 · see citing works
Relativistic quantum optics: The relativistic invariance of the light-matter interaction models
Martín-Martínez, E., & Rodriguez-López, P. (2018) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.97.105026 · Cited by 70 · see citing works
A modal ontology of properties for quantum mechanics
da Costa, N. C. A., Lombardi, O., & Lastiri, M. (2012) · Synthese · doi:10.1007/s11229-012-0218-4 · Cited by 68 · see citing works
“u n co rr ec te d p ro o f Synthese the textbooks on the matter (an exception is Ballentine (1998)).”
BackgroundTheoretical X‐ray spectroscopy of transition metal compounds
Bokarev, S. I., & Kühn, O. (2019) · Wiley Interdisciplinary Reviews Computational Molecular Science · doi:10.1002/wcms.1433 · Cited by 66 · see citing works
“However, the spectra could be equivalently expressed in as Fourier transforms of multitime dipole correlation functions.(45) For instance for XAS, these are two-point and for RIXS four-point dipole correlation functions.”
MethodDuprat, C., Giorgiutti-Dauphiné, F., Tseluiko, D., et al. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.234501 · Cited by 66 · see citing works
Probability out of Determinism
Strevens, M. (2011) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780199577439.003.0013 · Cited by 65 · see citing works
Fock parafermions and self-dual representations of the braid group
Cobanera, E., & Ortiz, G. (2014) · Physical Review A · doi:10.1103/physreva.89.012328 · Cited by 63 · see citing works
Transverse spin-orbit force in the spin Hall effect in ballistic semiconductor wires
Nikolić, B. K., Zârbo, L. P., & Welack, S. (2005) · Physical Review B · doi:10.1103/physrevb.72.075335 · Cited by 62 · see citing works
Scalar quantum kinetic theory for spin-1/2 particles: mean field theoryPreprint
Zamanian, J., Marklund, M., & Brodin, G. (2016) · Cited by 61 · see citing works
Raedt, H. A. D., Raedt, K. D., Michielsen, K. F. L., Keimpema, K., & Miyashita, S. (2007) · Journal of Computational and Theoretical Nanoscience · doi:10.1166/jctn.2007.2381 · Cited by 53 · see citing works
Analysis of multipath interference in three-slit experiments
Raedt, H. A. D., Michielsen, K. F. L., & Hess, K. (2012) · Physical Review A · doi:10.1103/physreva.85.012101 · Cited by 57 · see citing works
A local realist model for correlations of the singlet state
Raedt, K. D., Keimpema, K., Raedt, H. A. D., Michielsen, K. F. L., & Miyashita, S. (2006) · The European Physical Journal B · doi:10.1140/epjb/e2006-00364-9 · Cited by 52 · see citing works
Baily, C., & Finkelstein, N. D. (2015) · Physical Review Special Topics - Physics Education Research · doi:10.1103/physrevstper.11.020124 · Cited by 60 · see citing works
Network susceptibilities: Theory and applications
Manik, D., Rohden, M., Ronellenfitsch, H., et al. (2017) · Physical review. E · doi:10.1103/physreve.95.012319 · Cited by 57 · see citing works
Wave-particle duality of solitons and solitonic analog of the Ramsauer-Townsend effect
Belyaeva, T. L., & Serkin, V. N. (2012) · The European Physical Journal D · doi:10.1140/epjd/e2012-30214-2 · Cited by 56 · see citing works
“Notice that different misinterpretations of Ehrenfest’s theorem have been discussed in details in [32,33], where, in particular, it was shown that Ehrenfest’s theorem is neither necessary nor sufficient to characterize the classical regime.”
BackgroundBorn in an infinite universe: A cosmological interpretation of quantum mechanics
Aguirre, A. N., & Tegmark, M. (2011) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.84.105002 · Cited by 57 · see citing works
“, [1]) include the Ensemble [2, 3], Copenhagen [4, 5], Instrumental [6–9], Hydrodynamic [10], Consciousness [12–15], Bohm [16], Quantum Logic [17], Many-Worlds [18, 19], Stochastic Mechanics [20], Many-Minds [21, 22], Consistent Histories [23], Objective Collapse [24], Transactional [25], Modal [26], Existential [27],…”
BackgroundDecoherence time in self-induced decoherence
Castagnino, M., & Lombardi, O. (2005) · Physical Review A · doi:10.1103/physreva.72.012102 · Cited by 55 · see citing works
Nonlinear hydrodynamics of axion dark matter: Relative velocity effects and quantum forces
Marsh, D. J. E. (2015) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.91.123520 · Cited by 55 · see citing works
Extended Boole-Bell Inequalities Applicable to Quantum Theory
Raedt, H. A. D., Hess, K., & Michielsen, K. F. L. (2011) · Journal of Computational and Theoretical Nanoscience · doi:10.1166/jctn.2011.1781 · Cited by 55 · see citing works
“According to the axioms of quantum theory [ 31 ], repeated measurements on the system described by the normalized state vector |Ψ i yield statistical estimates for the single-particle expectation va lues E (2) 1 = h Ψ |σ1 � a|Ψ i ,”
BackgroundON THE VALIDITY OF BORN APPROXIMATION
Li, J., Wang, X., & Wang, T. (2010) · Electromagnetic waves · doi:10.2528/pier10070504 · Cited by 55 · see citing works
Khrennikov, A. Y., & Alodjants, A. P. (2019) · Entropy · doi:10.3390/e21020157 · Cited by 51 · see citing works
“MDZ, respectively. 1.3 Conditional probability approach The basic distinguishing feature of MKH is taking into account the conditional nature of quantum probabilities. Generally, we follow Ballentine [39, 40], especially his paper [41]. In the previous works [30], [31] and the present paper conditioning is modeled wit…”
InfluentialQuantum Mechanics: Modal Interpretation and Galilean Transformations
Ardenghi, J. S., Castagnino, M., & Lombardi, O. (2009) · Foundations of Physics · doi:10.1007/s10701-009-9313-x · Cited by 54 · see citing works
“And this, in turn, amounts to the breaking of the full validity of the Galilean group under the form of (8); then, the commutation relations involving the Hamiltonian ((8g), (8h) and (8i )) are, in general, no longer valid (see [10]).”
BackgroundInfluentialPearle, P. (2006) · Cited by 54 · see citing works
The modal-Hamiltonian interpretation and the Galilean covariance of quantum mechanics
Lombardi, O., Castagnino, M., & Ardenghi, J. S. (2010) · Studies in History and Philosophy of Science Part B Studies in History and Philosophy of Modern Physics · doi:10.1016/j.shpsb.2010.02.002 · Cited by 53 · see citing works
Hybrid classical-quantum formulations ask for hybrid notions
Barceló, C., Carballo-Rubio, R., Garay, L. J., et al. (2012) · Physical Review A · doi:10.1103/physreva.86.042120 · Cited by 52 · see citing works
Measures of spatial entanglement in a two-electron model atom
Pipek, J., & Nagy, I. (2009) · Physical Review A · doi:10.1103/physreva.79.052501 · Cited by 51 · see citing works
Belot, G. (2005) · Philosophy of Science · doi:10.1086/428072 · Cited by 50 · see citing works
Fermi’s golden rule: its derivation and breakdown by an ideal model
Zhang, J., & Liu, Y. (2016) · European Journal of Physics · doi:10.1088/0143-0807/37/6/065406 · Cited by 50 · see citing works
One-dimensional thermal properties of the Kemmer oscillator
Boumali, A. (2007) · Physica Scripta · doi:10.1088/0031-8949/76/6/014 · Cited by 49 · see citing works
Quantum theory as the most robust description of reproducible experiments
Raedt, H. A. D., Katsnelson, M. I., & Michielsen, K. F. L. (2014) · Annals of Physics · doi:10.1016/j.aop.2014.04.021 · Cited by 49 · see citing works
“On the other hand, there is no conflict with the statistical interpretation [82,103] if we ignore the conceptual difference between i-probs and ‘‘mathematical’’ probabilities.”
BackgroundMethodInfluentialPatra, M., & Maiti, S. K. (2017) · Scientific Reports · doi:10.1038/s41598-017-14499-2 · Cited by 49 · see citing works
Rutherford scattering of electron vortices
Boxem, R. V., Partoens, B., & Verbeeck, J. (2014) · Physical Review A · doi:10.1103/physreva.89.032715 · Cited by 50 · see citing works
Quantum mechanics as classical physics
Sebens, C. T. (2015) · Philosophy of Science · doi:10.1086/680190 · Cited by 48 · see citing works
“…t).17 The invariance of QM under Galilean boosts is sometimes demonstrated by showing that, for certain potentials, there exists a transformation of the state which appropriately shifts the probability density and guarantees satisfaction of the Schrödinger equation (e.g., Ballentine, 1998, §4.3).”
BackgroundInfluentialRaedt, H. A. D., Raedt, K. D., Michielsen, K. F. L., Keimpema, K., & Miyashita, S. (2007) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.76.104005 · Cited by 42 · see citing works
Matters are not so clear on the physical side
Lombardi, O., & Castagnino, M. (2010) · Foundations of Chemistry · doi:10.1007/s10698-010-9090-9 · Cited by 47 · see citing works
Entanglement and tensor product decomposition for two fermions
Caban, P., Podlaski, K., Rembieliński, J., Smoliński, K. A., & Walczak, Z. (2005) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/38/6/l02 · Cited by 46 · see citing works
ANY l-STATE ANALYTICAL SOLUTIONS OF THE KLEIN–GORDON EQUATION FOR THE WOODS–SAXON POTENTIAL
Badalov, V. H., AHMADOV, H. I., & Badalov, S. V. (2010) · International Journal of Modern Physics E · doi:10.1142/s0218301310015862 · Cited by 46 · see citing works
Partial Traces in Decoherence and in Interpretation: What Do Reduced States Refer to?
Fortin, S., & Lombardi, O. (2014) · Foundations of Physics · doi:10.1007/s10701-014-9791-3 · Cited by 45 · see citing works
“…Here we will not discuss the question of the supposed priority of pure states over mixed states: following certain presentations of the theory (e.g. Ballentine 1998), we will take the generic stance of considering state operators as representing quantum states, and pure states as a particular case.”
BackgroundResultInfluentialFortín, S., Lombardi, O., & González, J. C. M. (2016) · Foundations of Chemistry · doi:10.1007/s10698-016-9251-6 · Cited by 45 · see citing works
“…on identical systems with the same initial conditions, it is possible to define an ensemble, analogously to classical statistical mechanics (Ballentine 1998): the state of the ensemble after collapse can be represented by means of a density operator: 1 1 ˆ 2 2 measured L L R R (12) The…”
BackgroundWhy molecular structure cannot be strictly reduced to quantum mechanics
González, J. C. M., Fortín, S., & Lombardi, O. (2018) · Foundations of Chemistry · doi:10.1007/s10698-018-9310-2 · Cited by 45 · see citing works
“But now the atom is no longer free; it is a new system with a Hamiltonian that includes the magnetic field and whose eigenvalues depend explicitly on lm (see Ballentine 1998, p. 326).”
BackgroundOptimal uncertainty relations for extremely coarse-grained measurements
Rudnicki, Ł., Walborn, S. P., & Toscano, F. (2012) · Physical Review A · doi:10.1103/physreva.85.042115 · Cited by 43 · see citing works
Enabling quantum non-Markovian dynamics by injection of classical colored noise
Costa-Filho, J. I., Lima, R. B. B., de Paiva, R. R., Soares, P. M., Morgado, W. A. M., Franco, R. L., & Soares-Pinto, D. O. (2017) · Physical Review A · doi:10.1103/physreva.95.052126 · Cited by 45 · see citing works
“The Liouville-von Neumann equation [79] for the Hamiltonian in Eq.”
MethodQ-spaces and the foundations of quantum mechanics
Domenech, G., Holik, F., & Krause, D. (2008) · Americanae (AECID Library) · Cited by 43 · see citing works
Deterministic event-based simulation of quantum phenomena
Raedt, K. D., Raedt, H. A. D., & Michielsen, K. F. L. (2005) · Computer Physics Communications · doi:10.1016/j.cpc.2005.04.012 · Cited by 44 · see citing works
“the arrival of a single electron at a particular position on the detection screen [2, 4, 7, 8].”
BackgroundMethodInfluentialThe Merli–Missiroli–Pozzi Two-Slit Electron-Interference Experiment
Rosa, R. (2012) · Physics in Perspective · doi:10.1007/s00016-011-0079-0 · Cited by 44 · see citing works
Geiger–Nuttall law for Schrödinger solitons
Serkin, V. N., Hasegawa, A., & Belyaeva, T. L. (2013) · Journal of Modern Optics · doi:10.1080/09500340.2012.753478 · Cited by 42 · see citing works
“Notice that different misinterpretations of Ehrenfest’s theorem have been discussed in details by Ballentine with coauthors in [42,43], where, in particular, it was shown that Ehrenfest’s theorem is neither necessary nor sufficient to characterize the classical regime.”
BackgroundBernardini, A. E., & Orfeu Bertolami, A. (2013) · Physical Review A · doi:10.1103/physreva.88.012101 · Cited by 42 · see citing works
“[56]), and it is also discussed in Ref.”
BackgroundEvent-based simulation of single-photon beam splitters and Mach-Zehnder interferometers
Raedt, H. A. D., Raedt, K. D., & Michielsen, K. F. L. (2005) · Europhysics Letters (EPL) · doi:10.1209/epl/i2004-10443-7 · Cited by 42 · see citing works
“Although quantum theory gives us a recipe to compute the frequency for observing different types of events, it does not describe individual events [2,4,5].”
BackgroundEvent-Based Corpuscular Model for Quantum Optics Experiments
Michielsen, K. F. L., Jin, F., & Raedt, H. A. D. (2011) · Journal of Computational and Theoretical Nanoscience · doi:10.1166/jctn.2011.1783 · Cited by 43 · see citing works
Wiebe, N., & Ballentine, L. E. (2005) · Physical Review A · doi:10.1103/physreva.72.022109 · Cited by 42 · see citing works
Self-citation
- Authors
- Ballentine, L. E.
- Affiliations
- Simon Fraser University (CA)
- Corresponding author
- Ballentine, Leslie E
- Venue
- WORLD SCIENTIFIC eBooks
- Publisher
- WORLD SCIENTIFIC
- Published
- 1998-03
- DOI
- 10.1142/3142
- OpenAlex
- W1479923323
- Cited by
- 984
- References
- 0
- Citations by year
- 2026: 31 · 2025: 19 · 2024: 15 · 2023: 15 · 2022: 32 · 2021: 35 · 2020: 38 · 2019: 50 · 2018: 39 · 2017: 45 · 2016: 63 · 2015: 35 · 2014: 58 · 2013: 66 · 2012: 58
- FWCI
- 1.50
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- WORLD SCIENTIFIC eBooks (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Social Sciences › Arts and Humanities › History and Philosophy of Science › Philosophy and History of Science
- Keywords
- quantum foundations, interpretation of quantum mechanics, quantum mechanics textbook, philosophy of physics, quantum mechanics
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
