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

Access to Document

10.1007/3-540-27056-6_32

Cite this

@inbook{b13f1662cabb46fe9ce801e78e6335bb,

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.",

author = "Lieb, {Elliott H.} and Yau, {Horng Tzer}",

year = "2005",

doi = "10.1007/3-540-27056-6_32",

language = "English (US)",

isbn = "3540420835",

pages = "443--470",

booktitle = "The Stability of Matter",

publisher = "Springer Berlin Heidelberg",

}

TY - CHAP

T1 - The Chandrasekhar theory of stellar collapse as the limit of quantum mechanics

AU - Lieb, Elliott H.

AU - Yau, Horng Tzer

PY - 2005

Y1 - 2005

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.

UR - http://www.scopus.com/inward/record.url?scp=84892243639&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84892243639&partnerID=8YFLogxK

U2 - 10.1007/3-540-27056-6_32

DO - 10.1007/3-540-27056-6_32

M3 - Chapter

AN - SCOPUS:84892243639

SN - 3540420835

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

Access to Document

Other files and links

Fingerprint

Cite this