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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.
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“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]
In the citing paper
“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]
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“If quantum theory is assumed to describe the operation of the device, each measurement constitutes a statistically independent trial [10].”
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“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.”
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“…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).”
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A modal ontology of properties for quantum mechanics
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“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.”
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“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
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“, [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],…”
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BackgroundON THE VALIDITY OF BORN APPROXIMATION
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InfluentialQuantum Mechanics: Modal Interpretation and Galilean Transformations
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“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]).”
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“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.”
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Rutherford scattering of electron vortices
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Quantum mechanics as classical physics
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“…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).”
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Matters are not so clear on the physical side
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ANY l-STATE ANALYTICAL SOLUTIONS OF THE KLEIN–GORDON EQUATION FOR THE WOODS–SAXON POTENTIAL
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Partial Traces in Decoherence and in Interpretation: What Do Reduced States Refer to?
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“…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.”
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“…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
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“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
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Enabling quantum non-Markovian dynamics by injection of classical colored noise
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“The Liouville-von Neumann equation [79] for the Hamiltonian in Eq.”
MethodQ-spaces and the foundations of quantum mechanics
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Deterministic event-based simulation of quantum phenomena
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“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
Geiger–Nuttall law for Schrödinger solitons
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“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.”
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“[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
“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
Wiebe, N., & Ballentine, L. E. (2005) · Physical Review A · doi:10.1103/physreva.72.022109 · Cited by 41
Self-citation
Metadata
- 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 › Nuclear and High Energy Physics › Noncommutative and Quantum Gravity Theories
- Social Sciences › Arts and Humanities › History and Philosophy of Science › Philosophy of Biology and Scientific Explanation
- Keywords
- quantum foundations, interpretation of quantum mechanics, quantum mechanics textbook, philosophy of physics, quantum mechanics
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