000			03661nam a22004695i 4500
001			978-0-387-26369-4
003			DE-He213
005			20250710083936.0
007			cr nn 008mamaa
008			100301s2005 xxu| s |||| 0|eng d
020			_a9780387263694 _a99780387263694
024	7		_a10.1007/b136359 _2doi
082	0	4	_a512.2 _223
100	1		_aSinger, Stephanie Frank. _eauthor.
245	1	0	_aLinearity, Symmetry, and Prediction in the Hydrogen Atom _h[recurso electrónico] / _cby Stephanie Frank Singer.
264		1	_aNew York, NY : _bSpringer New York, _c2005.
300			_aXIV, 398 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_arecurso en línea _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aUndergraduate Texts in Mathematics, _x0172-6056
505	0		_aSetting the Stage -- Linear Algebra over the Complex Numbers -- Complex Scalar Product Spaces (a.k.a. Hilbert Spaces) -- Lie Groups and Lie Group Representations -- New Representations from Old -- Irreducible Representations and Invariant Integration -- Representations and the Hydrogen Atom -- The Algebra so(4) Symmetry of the Hydrogen Atom -- The Group SO(4) Symmetry of the Hydrogen Atom -- Projective Representations and Spin -- Independent Events and Tensor Products.
520			_aThe predictive power of mathematics in quantum phenomena is one of the great intellectual successes of the 20th century. This textbook, aimed at undergraduate or graduate level students (depending on the college or university), concentrates on how to make predictions about the numbers of each kind of basic state of a quantum system from only two ingredients: the symmetry and the linear model of quantum mechanics. This method, involving the mathematical area of representation theory or group theory, combines three core mathematical subjects, namely, linear algebra, analysis and abstract algebra. Wide applications of this method occur in crystallography, atomic structure, classification of manifolds with symmetry, and other areas. The topics unfold systematically, introducing the reader first to an important example of a quantum system with symmetry, the single electron in a hydrogen atom. Then the reader is given just enough mathematical tools to make predictions about the numbers of each kind of electronic orbital based solely on the physical spherical symmetry of the hydrogen atom. The final chapters address the related ideas of quantum spin, measurement and entanglement. This user-friendly exposition, driven by numerous examples and exercises, requires a solid background in calculus and familiarity with either linear algebra or advanced quantum mechanics. Linearity, Symmetry, and Prediction in the Hydrogen Atom will benefit students in mathematics, physics and chemistry, as well as a literate general readership. A separate solutions manual is available to instructors.
650		0	_aMATHEMATICS.
650		0	_aGROUP THEORY.
650		0	_aMATHEMATICAL PHYSICS.
650		0	_aMECHANICS.
650	1	4	_aMATHEMATICS.
650	2	4	_aGROUP THEORY AND GENERALIZATIONS.
650	2	4	_aMATHEMATICAL METHODS IN PHYSICS.
650	2	4	_aAPPLICATIONS OF MATHEMATICS.
650	2	4	_aMECHANICS.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387246376
830		0	_aUndergraduate Texts in Mathematics, _x0172-6056
856	4	0	_uhttp://dx.doi.org/10.1007/b136359 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c56570 _d56570