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

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 21
Author(s):  
Ilya G. Kaplan
Keyword(s):  
Wave Function ◽  
Pauli Exclusion Principle ◽  
Wave Functions ◽  
Total Wave Function ◽  
Exclusion Principle ◽  
Permutation Symmetry ◽  
Important Conclusion ◽  
Integer Spin ◽  
Total Wave ◽  
Symmetric Wave

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.

Resonant electron scattering by atoms

1963 ◽  
Vol 274 (1357) ◽  
pp. 253-266 ◽  
Keyword(s):  
Wave Function ◽  
Electron Scattering ◽  
Atomic Hydrogen ◽  
Resonant State ◽  
Wave Functions ◽  
Exclusion Principle ◽  
Inelastic Threshold ◽  
Atomic Systems ◽  
Resonance Energies ◽  
Resonant Electron

The Kapur-Peierls resonance formalism adapted for electron scattering by atomic systems is modified to allow for the exclusion principle, and a variational principle is derived for calculating the complex resonance energies. The theory is applied to calculate the first four resonance levels in the 1 S state of the electron/atomic hydrogen system by using a trial wave function made up from singleparticle functions which are modified (1 s ), (2 s ) and (2 p ) hydrogen wave functions. We find two levels (at approximately — 13 and — 10 eV) whose widths are of the order of a few volts. There are also two levels (at about — 3 and 0 eV) which have very narrow widths, less than 10 -2 eV, if they occur below the inelastic threshold, shooting up to widths of several volts at threshold. Such a narrow level occurs if the resonant state is energetically unable to decay to a state of the residual atom of which it contains a substantial component.

scholarly journals Beyond Quantum Mechanics? Hunting the `Impossible' Atoms --- Pauli Exclusion Principle Violation and Spontaneous Collapse of the Wave Function at Test

2015 ◽  
Vol 46 (1) ◽  
pp. 147 ◽  
Author(s):  
K. Piscicchia ◽  
C. Curceanu ◽  
S. Bartalucci ◽  
A. Bassi ◽  
S. Bertolucci ◽  
...  
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Pauli Exclusion Principle ◽  
Exclusion Principle

scholarly journals The exclusion priniciple and aperiodic systems

1929 ◽  
Vol 125 (796) ◽  
pp. 222-230 ◽  
Keyword(s):  
Wave Function ◽  
Helium Atom ◽  
Open Systems ◽  
Finite Energy ◽  
Energy Difference ◽  
Wave Functions ◽  
Exclusion Principle ◽  
Great Success ◽  
Stationary States ◽  
Closed Systems

Section I .—The exclusion principle of Pauli was introduced into the old quantum theory as an empirical fact that had been brought to light in the ordering of spectra. The new mechanics has provided some sort of explanation of the principle, for in a closed system with many electrons the mathematically possible stationary states can be separated into a number of groups, with the property that transitions between stationary states in different groups cannot occur. One of these group is made up of the stationary states corresponding occur. One of the these groups is made up of the stationary states corresponding to wave functions that are antisymmetrical in the co-ordinates of the electrons. Apart from accidental degeneracies, the stationary states in different groups have different energy values. The exclusion principle then states that only energy values belonging to the antisymmertical group are found in nature. The exclusion principle has had great success not only in explaining the spectra of helium and of more complicated atoms, but also, under the form of the Fermi-Dirac statistics, in accounting for metallic conduction and ferromagnetism. In all these phenomena we are dealing with systems is stationary states, possessing energy values which are discrete, although they may lie very close together. Now, as was first emphasised by Oppenheimer, we must also use antisymmetrical wave-functions to describe aperiodic phenomena, such as the collision between an electron and an atom. If we do not, we obtain probabilities for the formation of atoms whose wave-funtions are not antisymmetrical, as we shall show in section 4, where we consider the collision between an electron and a helium atom. A helium atom described by a symmetrical wave-function would show a singlet series in palce of the observed triplets and triplet series in place of the observed singlets. The wave-functions of open systems are essentially degenerate; the symmetical and antisymmetrical solution are not separated from one another by a finite energy difference; but for any arbitrary value of the energy (and of the other integrals of the motion) we can form a symmetrical and an antisymmetrical solution. This is somewhat fundamental difference between open and closed systems. For closed systems containing two electrons there exist only the symmetrical and the antisymmetical solution; but for open systems we might take any combination of the two. In fact, to describe an observable phenomenon such as a collision, the wave-function that it would first occur to us to use is a combination of the two. To fix our ideas we shall discuss the collision between two electrons. Our arguments could equally well be applied to the collision between an electron and a hydrogen atom, the problem originally discussed by Born; but the former is the simpler case, and perhaps illustrates our theory better.

Theoretical Oscillator Strengths for nP → nD Transitions in Mg

1975 ◽  
Vol 53 (2) ◽  
pp. 184-191 ◽  
Author(s):  
Charlotte Froese Fischer
Keyword(s):  
Wave Function ◽  
Total Wave Function ◽  
Oscillator Strengths ◽  
Total Wave

Theoretical oscillator strengths for the transitions 3s np1,3P → 3s md1,3D of Mg are reported for n = 3,4, … and m = 3,4,…The results are based on an MCHF approximation to the total wave function which includes the correlation of the outer two electrons.

scholarly journals The calculation of the terms of the optical spectrum of an atom with one series electron

1932 ◽  
Vol 138 (836) ◽  
pp. 550-579 ◽  
Keyword(s):  
Wave Function ◽  
Body Problem ◽  
Wave Functions ◽  
Exclusion Principle ◽  
Central Field ◽  
Many Body ◽  
Artificial System ◽  
Solutions Of Equations ◽  
Roman Letter

1. The theoretical determination of the energies of the stationary states of an atomic system is bound up with the solution of the many-body problem— in particular, with the determination of wave functions of many-electron atoms. An exact solution is not known, but approximations to it have been made by Hartree, Slater, Fock and Lennard-Jones.§ The method adopted is to replace the physical problem by an artificial one which admits of a solution, e. g., Hartree replaces the actual many-body problem by a one-body problem with a central field for each electron. Generally, the Schrodinger equation for an atom of nuclear charge N is { N Ʃ i = 1 (-1/2∇ i 2 -N/ r i ) + N Ʃ i > j = 1/ r ij -E} Ψ = 0, using atomic units11 and the usual notation. The artificial system replacing (1.1) has the equation { N Ʃ i = 1 (-1/2∇ i 2 - v i ) -E} ψ = 0, V i being a function of the co-ordinates of the i th. electron only. Equation (1.2) is separable, and reduces to equations of the type {-1/2∇ i 2 - v i ) -E i } ψ = 0, in the space co-ordinates of the - i th electron alone. If the solutions of equations (1. 3) are Ψ(α∣1), Ψ(π|p), where the Greek letter is the label of the wave function, and the numeral or Roman letter indicates the electron whose co-ordinates are substituted, then a solution of (1. 2) is ψ = Ψ(α∣1) Ψ (β∣2)....Ψ(π|p). The form of wave function which must be assumed in order to satisfy Pauli’s Exclusion Principle and be antisymmetric in the co-ordinates of all pairs of electrons, is the determinantal form Ψ = ∣ψ = Ψ(α∣1) Ψ (α∣2)....Ψ(α| p ) ∣ ∣ψ = Ψ(β∣1) Ψ (β∣2)....Ψ(β| p ) ∣ .................................................. ∣ψ = Ψ(π∣1) Ψ (π∣2)....Ψ(π| p ) ∣ which is the sum of the expressions obtained by permuting the co-ordinates 1, 2,........., p in the product (1. 4) and taking account of the signs of the permuta­tions. Thus we obtain an approximate wave function for the whole atom in terms of the one-electron wave functions.

Theoretical Oscillator Strengths for nS–mP Transitions in Mg

1975 ◽  
Vol 53 (4) ◽  
pp. 338-342 ◽  
Author(s):  
Charlotte Froese Fischer
Keyword(s):  
Wave Function ◽  
Total Wave Function ◽  
Oscillator Strengths ◽  
Total Wave

Theoretical oscillator strengths for the 3s ns1,3S–3s mp1,3P transitions of Mg are reported for n,m = 3,4,…,7.The results are based on an MCHF approximation to the total wave function which includes the correlation of the outer two electrons.

Hunting the "impossible atoms" Pauli exclusion principle violation and spontaneous collapse of the wave function at test

2014 ◽  
Vol 12 (07n08) ◽  
pp. 1560012
Author(s):  
Catalina Curceanu ◽  
Sergio Bartalucci ◽  
Angelo Bassi ◽  
Sergio Bertolucci ◽  
Carolina Berucci ◽  
...  
Keyword(s):  
Wave Function ◽  
Foundations Of Quantum Mechanics ◽  
Pauli Exclusion Principle ◽  
Exclusion Principle ◽  
X Rays ◽  
Experimental Apparatus ◽  
Lively Debate ◽  
Spontaneous Localization ◽  
Continuous Spontaneous Localization ◽  
Actual Limit

The Pauli exclusion principle (PEP) and, more generally, the spin-statistics connection, are at the very basis of our understanding of matter, life and Universe. The PEP spurs, presently, a lively debate on its possible limits, deeply rooted in the very foundations of Quantum Mechanics. It is, therefore, extremely important to test the limits of its validity. The Violation of the PEP (VIP) experiment established the best limit on the probability that PEP is violated by electrons, using the method of searching for PEP forbidden atomic transitions in copper. We describe the experimental method, the obtained results, and plans to go beyond the actual limit by upgrading the experimental apparatus. We discuss the possibility of using a similar experimental technique to search for X-rays as a signature of the spontaneous collapse of the wave function predicted by continuous spontaneous localization (CSL) theories.

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