Permutation Symmetry of Many-Particle Wave Functions

1965 ◽  
Vol 139 (2B) ◽  
pp. B500-B508 ◽  
Author(s):  
M. D. Girardeau
Keyword(s):  
Wave Functions ◽  
Permutation Symmetry

scholarly journals Symmetries in subatomic multi-quark systems

2018 ◽  
Vol 27 (12) ◽  
pp. 1840003
Author(s):  
J. D. Vergados ◽  
D. Strottman
Keyword(s):  
Quantum Chromodynamics ◽  
Quark Model ◽  
Spin Symmetry ◽  
Wave Functions ◽  
Low Energy ◽  
Isospin Symmetry ◽  
Permutation Symmetry

We discus the role of Quantum Chromodynamics (QCD) in low energy phenomena involving the color-spin symmetry of the quark model. We then combine it with orbital and isospin symmetry to obtain wave functions with the proper permutation symmetry, focusing on multi-quark systems.

scholarly journals The Valence-Bond (VB) Model and Its Intimate Relationship to the Symmetric or Permutation Group

Molecules ◽  
2021 ◽  
Vol 26 (15) ◽  
pp. 4524
Author(s):  
Marco Antonio Chaer Nascimento
Keyword(s):  
Permutation Group ◽  
Point Group ◽  
Valence Bond ◽  
Fundamental Difference ◽  
Wave Functions ◽  
Group Symmetry ◽  
Chemical Bonds ◽  
Permutation Symmetry ◽  
Independent Entity ◽  
The Many

VB and molecular orbital (MO) models are normally distinguished by the fact the first looks at molecules as a collection of atoms held together by chemical bonds while the latter adopts the view that each molecule should be regarded as an independent entity built up of electrons and nuclei and characterized by its molecular structure. Nevertheless, there is a much more fundamental difference between these two models which is only revealed when the symmetries of the many-electron Hamiltonian are fully taken into account: while the VB and MO wave functions exhibit the point-group symmetry, whenever present in the many-electron Hamiltonian, only VB wave functions exhibit the permutation symmetry, which is always present in the many-electron Hamiltonian. Practically all the conflicts among the practitioners of the two models can be traced down to the lack of permutation symmetry in the MO wave functions. Moreover, when examined from the permutation group perspective, it becomes clear that the concepts introduced by Pauling to deal with molecules can be equally applied to the study of the atomic structure. In other words, as strange as it may sound, VB can be extended to the study of atoms and, therefore, is a much more general model than MO.

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.

scholarly journals APPROXIMATIONS OF SINGULAR VERTEX COUPLINGS IN QUANTUM GRAPHS

2007 ◽  
Vol 19 (06) ◽  
pp. 571-606 ◽  
Author(s):  
PAVEL EXNER ◽  
ONDŘEJ TUREK
Keyword(s):  
Boundary Conditions ◽  
Time Reversal ◽  
Wave Functions ◽  
Parameter Family ◽  
Quantum Graph ◽  
Quantum Graphs ◽  
Permutation Symmetry ◽  
Singular Case ◽  
Singular Vertex

We discuss approximations of the vertex coupling on a star-shaped quantum graph of n edges in the singular case when the wave functions are not continuous at the vertex and no edge-permutation symmetry is present. It is shown that the Cheon–Shigehara technique using δ interactions with nonlinearly scaled couplings yields a 2n-parameter family of boundary conditions in the sense of norm resolvent topology. Moreover, using graphs with additional edges, one can approximate the [Formula: see text]-parameter family of all time-reversal invariant couplings.

scholarly journals Spectrum of the $$uudc \bar{c}$$ hidden charm pentaquark with an SU(4) flavor-spin hyperfine interaction

2019 ◽  
Vol 79 (11) ◽  
Author(s):  
Fl. Stancu
Keyword(s):  
Hyperfine Interaction ◽  
Ground State ◽  
Constituent Quark ◽  
Constituent Quark Model ◽  
Negative Parity ◽  
Wave Functions ◽  
Positive Parity ◽  
Permutation Symmetry ◽  
Orbital Excitation ◽  
Space Wave

AbstractWe study a few of the lowest states of the pentaquark $$uudc\overline{c}$$uudcc¯, of positive and negative parity, in a constituent quark model with an SU(4) flavor-spin hyperfine interaction. For positive parity we introduce space wave functions of appropriate permutation symmetry with one unit of orbital angular momentum in the internal motion of the four-quark subsystem or an orbital excitation between the antiquark and the four quark subsystem which remains in the ground state. We show that the lowest positive parity states $$1/2^+, 3/2^+$$1/2+,3/2+ are provided by the first alternative and are located below the $$1/2^-$$1/2- and the $$1/2^+$$1/2+ states with all quarks in the ground state. We compare our results with the LHCb three narrow pentaquark structures reported in 2019.

Gaussian Wave Functions and the Many-Body Problem

1972 ◽  
Vol 50 (4) ◽  
pp. 305-311 ◽  
Author(s):  
R. L. Hall
Keyword(s):  
Bound States ◽  
Wave Functions ◽  
Permutation Symmetry ◽  
Many Body ◽  
Single Product ◽  
Gaussian Functions ◽  
Energy Expectation ◽  
The Many ◽  
Body Energy ◽  
Exact Energy

A system of identical nonrelativistic particles is considered. It is shown that the wave functions for relative motion, which have the correct permutation symmetry, must satisfy two functional equations. In the case of bosons these equations are solved for those bound states where the wave function is also in a single-product form. The only solutions are Gaussian functions. Consequently these are the only functions which can reduce the N-body energy expectation to an integral over a single variable. Furthermore, we show that our reduced two-body Hamiltonian which in general gives energy lower bounds yields the exact energy of the entire system only for the Hooke's law interaction. Neither possibility is allowed by fermions.

Magnetotunneling spectroscopy imaging of electron wave functions in self-assembled InAs quantum dots

2001 ◽  
Vol 171 (12) ◽  
pp. 1365
Author(s):  
E.E. Vdovin ◽  
Yu.N. Khanin ◽  
Yu.V. Dubrovskii ◽  
A. Veretennikov ◽  
A. Levin ◽  
...  
Keyword(s):  
Quantum Dots ◽  
Wave Functions ◽  
Electron Wave ◽  
Inas Quantum Dots ◽  
Self Assembled
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