Matches in SemOpenAlex for { <https://semopenalex.org/work/W3098895747> ?p ?o ?g. }
Showing items 1 to 99 of
99
with 100 items per page.
- W3098895747 abstract "The wave functions of Boson and Fermion gases are known even when the particles have harmonic interactions. Here we generalise these results by solving exactly the N-body Schrodinger equation for potentials V that can be any function of the sum of the squares of the distances of the particles from one another in 3 dimensions. For the harmonic case that function is linear in r^2. Explicit N-body solutions are given when U(r) = -2M hbar^{-2} V(r) = zeta r^{-1} - zeta_2 r^{-2}. Here M is the sum of the masses and r^2 = 1/2 M^{-2} Sigma Sigma m_I m_J ({bf x}_I - {bf x}_J)^2. For general U(r) the solution is given in terms of the one or two body problem with potential U(r) in 3 dimensions. The degeneracies of the levels are derived for distinguishable particles, for Bosons of spin zero and for spin 1/2 Fermions. The latter involve significant combinatorial analysis which may have application to the shell model of atomic nuclei. For large N the Fermionic ground state gives the binding energy of a degenerate white dwarf star treated as a giant atom with an N-body wave function. The N-body forces involved in these extraordinary N-body problems are not the usual sums of two body interactions, but nor are forces between quarks or molecules. Bose-Einstein condensation of particles in 3 dimensions interacting via these strange potentials can be treated by this method." @default.
- W3098895747 created "2020-11-23" @default.
- W3098895747 creator A5017109309 @default.
- W3098895747 creator A5084443812 @default.
- W3098895747 date "1999-09-08" @default.
- W3098895747 modified "2023-10-16" @default.
- W3098895747 title "Exact quantum solutions of extraordinary N -body problems" @default.
- W3098895747 cites W1963977249 @default.
- W3098895747 cites W1982428017 @default.
- W3098895747 cites W1983570084 @default.
- W3098895747 cites W1986348618 @default.
- W3098895747 cites W1990755516 @default.
- W3098895747 cites W1993834364 @default.
- W3098895747 cites W1998904626 @default.
- W3098895747 cites W2010271231 @default.
- W3098895747 cites W2011023754 @default.
- W3098895747 cites W2013969689 @default.
- W3098895747 cites W2033266183 @default.
- W3098895747 cites W2036113683 @default.
- W3098895747 cites W2037387493 @default.
- W3098895747 cites W2042561523 @default.
- W3098895747 cites W2047424724 @default.
- W3098895747 cites W2058352507 @default.
- W3098895747 cites W2067175118 @default.
- W3098895747 cites W2070484575 @default.
- W3098895747 cites W2074599834 @default.
- W3098895747 cites W2077033257 @default.
- W3098895747 cites W2078416031 @default.
- W3098895747 cites W2088536379 @default.
- W3098895747 cites W2089996117 @default.
- W3098895747 cites W2107495553 @default.
- W3098895747 cites W2129109538 @default.
- W3098895747 cites W2145207548 @default.
- W3098895747 cites W2151175174 @default.
- W3098895747 cites W2318462890 @default.
- W3098895747 cites W2372649670 @default.
- W3098895747 cites W2748333473 @default.
- W3098895747 cites W3104181811 @default.
- W3098895747 cites W3124313224 @default.
- W3098895747 cites W4242274835 @default.
- W3098895747 cites W4295023611 @default.
- W3098895747 doi "https://doi.org/10.1098/rspa.1999.0450" @default.
- W3098895747 hasPublicationYear "1999" @default.
- W3098895747 type Work @default.
- W3098895747 sameAs 3098895747 @default.
- W3098895747 citedByCount "8" @default.
- W3098895747 countsByYear W30988957472013 @default.
- W3098895747 countsByYear W30988957472014 @default.
- W3098895747 crossrefType "journal-article" @default.
- W3098895747 hasAuthorship W3098895747A5017109309 @default.
- W3098895747 hasAuthorship W3098895747A5084443812 @default.
- W3098895747 hasBestOaLocation W30988957472 @default.
- W3098895747 hasConcept C113603373 @default.
- W3098895747 hasConcept C121332964 @default.
- W3098895747 hasConcept C134306372 @default.
- W3098895747 hasConcept C33923547 @default.
- W3098895747 hasConcept C33980943 @default.
- W3098895747 hasConcept C35235930 @default.
- W3098895747 hasConcept C37914503 @default.
- W3098895747 hasConcept C52233224 @default.
- W3098895747 hasConcept C62520636 @default.
- W3098895747 hasConcept C63036615 @default.
- W3098895747 hasConcept C69523127 @default.
- W3098895747 hasConcept C72319582 @default.
- W3098895747 hasConcept C79118098 @default.
- W3098895747 hasConcept C84114770 @default.
- W3098895747 hasConceptScore W3098895747C113603373 @default.
- W3098895747 hasConceptScore W3098895747C121332964 @default.
- W3098895747 hasConceptScore W3098895747C134306372 @default.
- W3098895747 hasConceptScore W3098895747C33923547 @default.
- W3098895747 hasConceptScore W3098895747C33980943 @default.
- W3098895747 hasConceptScore W3098895747C35235930 @default.
- W3098895747 hasConceptScore W3098895747C37914503 @default.
- W3098895747 hasConceptScore W3098895747C52233224 @default.
- W3098895747 hasConceptScore W3098895747C62520636 @default.
- W3098895747 hasConceptScore W3098895747C63036615 @default.
- W3098895747 hasConceptScore W3098895747C69523127 @default.
- W3098895747 hasConceptScore W3098895747C72319582 @default.
- W3098895747 hasConceptScore W3098895747C79118098 @default.
- W3098895747 hasConceptScore W3098895747C84114770 @default.
- W3098895747 hasLocation W30988957471 @default.
- W3098895747 hasLocation W30988957472 @default.
- W3098895747 hasLocation W30988957473 @default.
- W3098895747 hasOpenAccess W3098895747 @default.
- W3098895747 hasPrimaryLocation W30988957471 @default.
- W3098895747 hasRelatedWork W1969098918 @default.
- W3098895747 hasRelatedWork W2036717655 @default.
- W3098895747 hasRelatedWork W2063139113 @default.
- W3098895747 hasRelatedWork W2074958934 @default.
- W3098895747 hasRelatedWork W2080767640 @default.
- W3098895747 hasRelatedWork W2087542360 @default.
- W3098895747 hasRelatedWork W2123962311 @default.
- W3098895747 hasRelatedWork W2787649653 @default.
- W3098895747 hasRelatedWork W4205224088 @default.
- W3098895747 hasRelatedWork W4298308748 @default.
- W3098895747 isParatext "false" @default.
- W3098895747 isRetracted "false" @default.
- W3098895747 magId "3098895747" @default.
- W3098895747 workType "article" @default.