Exclusion principle and indistinguishability of identical particles in quantum mechanics

Kaplan, I. G.

doi:10.1016/0022-2860(92)80032-d

Cited by 14 publications

(2 citation statements)

References 19 publications

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“…The indistinguishability principle is insensitive to the permutation symmetry of wavefunction and, as was shown above, it is satisfied by wavefunctions with arbitrary symmetry. Nevertheless, there are physical arguments [35,71,87], that the identical particle system may not be characterized by an arbitrary permutations symmetry. In next subsection we will discuss these arguments.…”

Section: Indistinguishability Of Identical Particles and The Symmetrimentioning

confidence: 99%

Modern State of the Pauli Exclusion Principle and the Problems of Its Theoretical Foundation

Kaplan

2020

Symmetry

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The Pauli exclusion principle (PEP) can be considered from two aspects. First, it asserts that particles that have half-integer spin (fermions) are described by antisymmetric wave functions, and particles that have integer spin (bosons) are described by symmetric wave functions. It is called spin-statistics connection (SSC). The physical reasons why SSC exists are still unknown. On the other hand, PEP is not reduced to SSC and can be consider from another aspect, according to it, the permutation symmetry of the total wave function can be only of two types: symmetric or antisymmetric. They both belong to one-dimensional representations of the permutation group, while other types of permutation symmetry are forbidden. However, the solution of the Schrödinger equation may have any permutation symmetry. We analyze this second aspect of PEP and demonstrate that proofs of PEP in some wide-spread textbooks on quantum mechanics, basing on the indistinguishability principle, are incorrect. The indistinguishability principle is insensitive to the permutation symmetry of wave function. So, it cannot be used as a criterion for the PEP verification. However, as follows from our analysis of possible scenarios, the permission of states with permutation symmetry more general than symmetric and antisymmetric leads to contradictions with the concepts of particle identity and their independence. Thus, the existence in our Nature particles only in symmetric and antisymmetric permutation states is not accidental, since all symmetry options for the total wave function, except the antisymmetric and symmetric, cannot be realized. From this an important conclusion follows, we may not expect that in future some unknown elementary particles that are not fermions or bosons can be discovered.

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Section: Indistinguishability Of Identical Particles and The Symmetrimentioning

confidence: 99%

Modern State of the Pauli Exclusion Principle and the Problems of Its Theoretical Foundation

Kaplan

2020

Symmetry

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“…In the next sections, we discuss the possible answers to this question, developing some ideas from our previous publications [32,33].…”

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Is the Pauli exclusive principle an independent quantum mechanical postulate?

Kaplan

2002

Int J of Quantum Chemistry

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Foundation of the Pauli exclusive principle is discussed. It isdemonstrated that the indistinguishability principle is insensitive to the permutation symmetry of the wave function and cannot be used as a criterion for the verification of the Pauli exclusive principle. The heuristic arguments are given in favor that the existence in nature of only the nondegenerate permutation representations (symmetrical and antisymmetrical) is not occasional. As follows from our analysis of possible scenarios, the permission of degenerate permutation representations leads to contradictions with the concept of particle identity and their independence. Thus, the prohibition of degenerate permutation states by the Pauli exclusive principle follows from the general physical assumptions inside quantum theory, but the problem of spinstatistics connection is still open. It is pointed out that the Pauli exclusive principle and the Jahn-Teller effect have some similar features.

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Locality and nonlocality in quantum mechanics: A two-proton EPR experiment

McWeeny

Amovilli

1999

Int. J. Quant. Chem.

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Two ''thought experiments'' are central to most discussions of the famous EPR paradox: Experiment 1, in which two electrons with spins initially coupled Ž to total spin S are carried apart to a great distance e.g., in a molecular dissociation . process , and Experiment 2, which is similar but refers to two bare protons. The crucial question to be asked is whether the spin coupling will be conserved at all distances: if it Ž is, then the system exhibits ''nonlocality'' the two particles stay ''correlated'' in some . way, even at infinite distance and thus violates Einstein's principle of locality-which denies that possibility. A recent discussion of Experiment 1 shows that nonlocality is the rule only up to a point at which the singlet᎐triplet interval is small enough to be bridged by weak interaction with the ''heat bath'' in which the system is embedded: Beyond that point, the system is no longer described by a wave function but instead by a statistical Ž . ensemble. When ensemble averaging is admitted, the spin-correlation function Q r , r c 1 2 decreases to zero at all points in space and the coupling is broken; the particles are then independent and neither can be influenced by its previous interaction with the other. In the present work, the same approach is used to discuss the two-proton system Ž . Experiment 2 . The conclusions are similar: The protons are described by appropriate wave packets, with an initial overlap sufficient to give a substantial singlet᎐triplet Ž separation ⌬ E, and, again, the spin coupling is broken when the overlap and, . consequently, ⌬ E decreases to a sufficiently small value. ᮊ 1999 John Wiley & Sons, Inc.Int J Quant Chem 74: 573᎐584, 1999 Key words: EPR experiment; spin correlation; density matrix; decoherence U Dedicated to George Hall-a master-builder of mathematical models.

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Exclusion principle and indistinguishability of identical particles in quantum mechanics

Cited by 14 publications

References 19 publications

Modern State of the Pauli Exclusion Principle and the Problems of Its Theoretical Foundation

Modern State of the Pauli Exclusion Principle and the Problems of Its Theoretical Foundation

Is the Pauli exclusive principle an independent quantum mechanical postulate?

Locality and nonlocality in quantum mechanics: A two-proton EPR experiment

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