The Chandrasekhar theory of stellar collapse as the limit of quantum mechanics

Elliott H. Lieb; Horng Tzer Yau

doi:10.1007/3-540-27056-6_32

The Chandrasekhar theory of stellar collapse as the limit of quantum mechanics

Elliott H. Lieb
, Horng Tzer Yau

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

1 Scopus citations

Abstract

Starting with a relativistic Schrödinger Hamiltonian for neutral gravitating particles, we prove that as the particle number N → ∞ and the gravitation constant G→0 we obtain the well known semiclassical theory for the ground State of stars. For fermions; the correct limit is to fix GW^2/3 and the Chandrasekhar formula is obtained. For bosons the correct limit is to fix GN and a Hartree type equation is obtained. In the fermion case we also prove that the semiclassical equation has a unique solution - a fact which had not been established previously.

Original language	English (US)
Title of host publication	The Stability of Matter
Subtitle of host publication	From Atoms to Stars: Fourth Edition
Publisher	Springer Berlin Heidelberg
Pages	443-470
Number of pages	28
ISBN (Print)	3540420835, 9783540222125
DOIs	https://doi.org/10.1007/3-540-27056-6_32
State	Published - 2005

All Science Journal Classification (ASJC) codes

General Physics and Astronomy

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10.1007/3-540-27056-6_32

Cite this

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title = "The Chandrasekhar theory of stellar collapse as the limit of quantum mechanics",

abstract = "Starting with a relativistic Schr{\"o}dinger Hamiltonian for neutral gravitating particles, we prove that as the particle number N → ∞ and the gravitation constant G→0 we obtain the well known semiclassical theory for the ground State of stars. For fermions; the correct limit is to fix GW2/3 and the Chandrasekhar formula is obtained. For bosons the correct limit is to fix GN and a Hartree type equation is obtained. In the fermion case we also prove that the semiclassical equation has a unique solution - a fact which had not been established previously.",

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AU - Lieb, Elliott H.

AU - Yau, Horng Tzer

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N2 - Starting with a relativistic Schrödinger Hamiltonian for neutral gravitating particles, we prove that as the particle number N → ∞ and the gravitation constant G→0 we obtain the well known semiclassical theory for the ground State of stars. For fermions; the correct limit is to fix GW2/3 and the Chandrasekhar formula is obtained. For bosons the correct limit is to fix GN and a Hartree type equation is obtained. In the fermion case we also prove that the semiclassical equation has a unique solution - a fact which had not been established previously.

AB - Starting with a relativistic Schrödinger Hamiltonian for neutral gravitating particles, we prove that as the particle number N → ∞ and the gravitation constant G→0 we obtain the well known semiclassical theory for the ground State of stars. For fermions; the correct limit is to fix GW2/3 and the Chandrasekhar formula is obtained. For bosons the correct limit is to fix GN and a Hartree type equation is obtained. In the fermion case we also prove that the semiclassical equation has a unique solution - a fact which had not been established previously.

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UR - https://www.scopus.com/pages/publications/84892243639#tab=citedBy

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M3 - Chapter

AN - SCOPUS:84892243639

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SN - 9783540222125

SP - 443

EP - 470

BT - The Stability of Matter

PB - Springer Berlin Heidelberg

ER -

The Chandrasekhar theory of stellar collapse as the limit of quantum mechanics

Abstract

All Science Journal Classification (ASJC) codes

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