Identical particles and the helium atom

2021 ◽  
pp. 164-178
Author(s):  
Geoffrey Brooker
Keyword(s):  
Wave Function ◽  
Helium Atom ◽  
Pauli Principle ◽  
Quantum States ◽  
Spin States ◽  
Identical Particles ◽  
Space Wave

“Identical particles and the helium atom” introduces bosons and fermions. Fermion states are expressed in terms of Slater determinants and the Pauli Principle. Helium is presented in such a way as to show what properties are and are not due to electron identity. Quantum states are described according as the space wave function is symmetric or antisymmetric under interchange of labels attached to the electrons. These in turn form singlet and triplet spin states when the electrons’ fermion identity is taken into account. Helium is an example of LS coupling, but a rather stunted example.

THE PAULI PRINCIPLE AND QUANTUM TRANSPORT

1994 ◽  
Vol 08 (21n22) ◽  
pp. 1377-1385 ◽  
Author(s):  
S.A. GURVITZ ◽  
H.J. LIPKIN ◽  
Ya. S. PRAGER
Keyword(s):  
Quantum Wells ◽  
Resonant Tunneling ◽  
Fock Space ◽  
Pauli Principle ◽  
Semiconductor Heterostructures ◽  
Rate Equations ◽  
Semiconductor Quantum Wells ◽  
Occupation Numbers ◽  
The One ◽  
Space Wave

A new method using Fock space wave functions is proposed for studying resonant tunneling in semiconductor quantum wells. The use of binary occupation numbers as dynamical variables, rather than properties of individual electrons, manifestly takes account of electron statistics, which enables investigation of the influence of the Pauli principle on resonant tunneling in the presence of inelastic scattering. Applied to the evaluation of the resonant current in semiconductor heterostructures, our approach predicts considerable deviations from the one-electron and rate equations pictures.

scholarly journals The Strange (Hi)story of Particles and Waves

2016 ◽  
Vol 71 (3) ◽  
pp. 195-212
Author(s):  
H. Dieter Zeh
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Excited States ◽  
Configuration Space ◽  
Historical Context ◽  
Quantum States ◽  
Wave Functions ◽  
General Readership ◽  
Boson Fields

AbstractThis is an attempt of a non-technical but conceptually consistent presentation of quantum theory in a historical context. While the first part is written for a general readership, Section 5 may appear a bit provocative to some quantum physicists. I argue that the single-particle wave functions of quantum mechanics have to be correctly interpreted as field modes that are “occupied once” (i.e. first excited states of the corresponding quantum oscillators in the case of boson fields). Multiple excitations lead to apparent many-particle wave functions, while the quantum states proper are defined by wave function(al)s on the “configuration” space of fundamental fields, or on another, as yet elusive, fundamental local basis.

MICROSCOPIC WAVE FUNCTION OF ALPHA CONDENSATION

2009 ◽  
Vol 24 (11) ◽  
pp. 2003-2018 ◽  
Author(s):  
AKIHIRO TOHSAKI ◽  
YASURO FUNAKI ◽  
HISASHI HORIUCHI ◽  
GERD RÖPKE ◽  
PETER SCHUCK ◽  
...  
Keyword(s):  
Wave Function ◽  
Pauli Principle ◽  
Numerical Results ◽  
Microscopic Model

We explain how to treat a microscopic wave function of α-condensation named THSR taking 3α-condensation as a typical example. The microscopic model, which fully takes into account the Pauli principle between all the constituent nucleons and effective inter-nucleon forces simultaneously, can play an important role in reproducing an α-gas-like nature thanks to α-condensation. We study its typical features by giving numerical results of the norm kernel for 3α-condensation.

The compressed helium atom variationally treated via a correlated Hylleraas wave function

2003 ◽  
Vol 307 (5-6) ◽  
pp. 326-336 ◽  
Author(s):  
N. Aquino ◽  
A. Flores-Riveros ◽  
J.F. Rivas-Silva
Keyword(s):  
Wave Function ◽  
Helium Atom

Quantum Nondeterministic Computation based on Statistics Superselection Rules

1997 ◽  
Vol 11 (10) ◽  
pp. 1297-1309
Author(s):  
G. Castagnoli
Keyword(s):  
Quantum States ◽  
Physical Situation ◽  
Identical Particles ◽  
Complete Problem ◽  
Np Complete

Quantum states which obey certain symmetry superselection rules under identical particles permutation can be interpreted as computational states satisfying corresponding Boolean predicates. Given the NP-complete problem of testing the satisfiability of a generic Boolean predicate P, we investigate the possibility of achieving quantum nondeterministic computation by deriving, from P, a physical situation in which the computational states satisfy Piff they satisfy a special fermion statistics.

Highly excited 1sns states of the helium atom

1976 ◽  
Vol 54 (10) ◽  
pp. 1543-1549 ◽  
Author(s):  
Mary Kuriyan ◽  
Huw O. Pritchard
Keyword(s):  
Wave Function ◽  
Helium Atom ◽  
Lower Energy ◽  
Computer Time ◽  
Suitable Choice ◽  
Triplet States ◽  
Astrophysical Interest ◽  
Variational Calculations ◽  
Singlet And Triplet States

Variational calculations are reported on the 1sns singlet and triplet states of the helium atom, up to and including n = 26. By suitable choice of terms in the expansion for the wave function, significant economies in computer time are possible, and we quote an example of a 12-term uncorrelated wave function which gives a lower energy than Pekeris' 220-term correlated wave function. The problems of extending these calculations to much higher n (e.g. n > 100) to include states of astrophysical interest are enumerated.

Correlated Atomic Pair Functions by the e-ϱ-Method. I. Ground State 11S and Lowest Excited States n1S (n > 1) and n3S of Helium

1999 ◽  
Vol 54 (12) ◽  
pp. 711-717
Author(s):  
F. F. Seelig ◽  
G. A. Becker
Keyword(s):  
Integral Equation ◽  
Wave Function ◽  
Helium Atom ◽  
Excited States ◽  
Ground State ◽  
Single Parent ◽  
Hartree Fock ◽  
Atomic Pair ◽  
Electronic Wave Function ◽  
S States

Abstract Some low n1S and n3S states of the helium atom are computed with the aid of the e-e method which formulates the electronic wave function of the 2 electrons ψ = e-e F, where ϱ=Z(r1+r2)–½r12 and here Z = 2. Both the differential and the integral equation for F contain a pseudopotential Ṽ instead of the true potential V that contrary to V is finite. For the ground state, F = 1 yields nearly the Hartree-Fock SCF accuracy, whereas a multinomial expansion in r1, r2 , r2 yields a relative error of about 10-7 . All integrals can be computed analytically and are derived from one single “parent” integral.

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