Quantum theory of magnetism:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Heidelberg [u.a.]
Springer
2009
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 752 S. graph. Darst. |
| ISBN: | 9783540854159 9783540854166 |
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| 100 | 1 | |a Nolting, Wolfgang |d 1944- |e Verfasser |0 (DE-588)115505261 |4 aut | |
| 245 | 1 | 0 | |a Quantum theory of magnetism |c Wolfgang Nolting and Anupuru Ramakanth |
| 264 | 1 | |a Heidelberg [u.a.] |b Springer |c 2009 | |
| 300 | |a XIII, 752 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Quantentheorie | |
| 650 | 4 | |a Magnetism | |
| 650 | 4 | |a Quantum theory | |
| 650 | 0 | 7 | |a Quantentheorie |0 (DE-588)4047992-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Magnetismus |0 (DE-588)4037021-5 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Quantentheorie |0 (DE-588)4047992-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Ramakanth, Anupuru |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016789931&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016789931 | ||
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| adam_text | Contents
1
Basic Facts
..................................................... 1
1.1
Macroscopic Maxwell Equations
............................. 1
1.2
Magnetic Moment and Magnetization
......................... 7
1.3
Susceptibility
............................................. 13
1.4
Classification of Magnetic Materials
.......................... 15
1.4.1
Diamagnetism
.................................... 15
1
.4.2
Paramagnetism
.................................... 15
1.4.3
Collective Magnetism
.............................. 17
1.5
Elements of Thermodynamics
............................... 19
1.6
Problems
................................................. 22
2
Atomic Magnetism
.............................................. 25
2.1
Hund s Rules
............................................. 25
2.1.1
Russell-Saunders (LS-) Coupling
.................... 25
2.1.2
Hund s Rules for
¿5
Coupling
....................... 27
2.2
Dirac Equation
............................................ 28
2.3
Electron Spin
............................................. 34
2.4
Spin-Orbit Coupling
....................................... 40
2.5
Wigner-Eckart Theorem
.................................... 45
2.5.1
Rotation
......................................... 45
2.5.2
Rotation Operator
................................. 47
2.5.3
Angular Momentum
............................... 48
2.5.4
Rotation Matrices
.................................. 50
2.5.5
Tensor Operators
.................................. 52
2.5.6
Wigner-Eckart Theorem
............................ 53
2.5.7
Examples of Application
............................ 55
2.6
Electron in an External Magnetic Field
........................ 56
2.7
Nuclear Quadrupole Field
................................... 62
2.8
Hyperfine Field
........................................... 67
2.9
Magnetic Hamiitonian of the Atomic Electron
.................. 72
2.10
Many-Electron Systems
.................................... 74
2.10.1
Coulomb Interaction
............................... 74
x
Contents
2.10.2
Spin-Orbit Coupling
............................... 75
2.10.3
Further Couplings
................................. 76
2.11
Problems
................................................. 81
3
Diamagnetism
................................................. 85
3.1
Bohr-van
Leeuwen
Theorem
................................ 85
3.2
Larmor Diamagnetism (Insulators)
........................... 87
3.3
The
Sommerfeld
Model of a Metal
........................... 90
3.3.1
Properties of the Model
............................. 91
3.3.2 Sommerfeld
Expansion
............................. 99
3.4
Landau Diamagnetism (Metals)
..............................104
3.4.1
Free Electrons in Magnetic Field (Landau Levels)
......104
3.4.2
Grand Canonical Potential of the Conduction Electrons
.. 109
3.4.3
Susceptibility of the Conduction Electrons
.............117
3.5
The
de Haas-Van Alphen
Effect
.............................121
3.5.1
Oscillations in the Magnetic Susceptibility
.............121
3.5.2
Electron Orbits in Magnetic Field
....................124
3.5.3
Physical Origin of the Oscillations
...................128
3.5.4
Onsager Argument
.................................131
3.6
Problems
.................................................134
References
......................................................136
4
Paramagnetism
.................................................137
4.1 Pauli
Spin Paramagnetism
..................................138
4.1.1
Primitive Theory of the
Pauli
Spin Paramagnetism
.... 138
4.1.2
Temperature Corrections
............................141
4.1.3
Exchange Corrections
..............................142
4.2
Paramagnetism of the Localized Electrons
.....................155
4.2.1
Weak Spin-Orbit Interaction
........................158
4.2.2
Strong Spin-Orbit Coupling
.........................164
4.2.3
Van Vleck Paramagnetism
..........................166
4.3
Problems
.................................................171
References
......................................................174
5
Exchange Interaction
............................................175
5.1
Phenomenological Theories
.................................178
5.1.1
The Exchange Field
................................178
5.1.2
Weiss Ferromagnet
................................180
5.2
Direct Exchange Interaction
.................................184
5.2.1
Pauli s Principle
...................................184
5.2.2
The Heitler-London Method
........................188
5.2.3
Dirac s Vector Model
...............................195
5.3
Indirect Exchange Interaction
................................200
5.3.1
Rudermann-Khtel-Kasuya-Yosida (RKKY) Interaction
. 200
5.3.2
Superexchange
....................................209
Contents xi
5.3.3 Double Exchange..................................217
5.4 Problems.................................................226
References
......................................................231
6 Ising Model ....................................................233
6.1 The Model ...............................................234
6.2
The One Dimensional
Ising Model...........................236
6.2.
t
Spontaneous Magnetization
.........................236
6.2.2
One Dimensional Ising Model in External Field
........240
6.3
The Phase Transition of Two-Dimensional Ising Model
..........245
6.3.1
The Method of Proof
...............................245
6.3.2
Finite Ising Lattice with Special Boundary Conditions
... 247
6.3.3
Probabilities
......................................247
6.3.4
Realization Possibilities for the Polygons
..............249
6.3.5
Magnetization of the Finite Lattice
...................252
6.3.6
Thermodynamic Limit
..............................252
6.4
The Free Energy of the Two-Dimensional Ising Model
...........254
6.4.1
High-Temperature Expansion
........................255
6.4.2
Spin Products as Graphs
............................256
6.4.3
Loops
...........................................257
6.4.4
Directed Paths
....................................261
6.4.5
Matrix Mt
........................................264
6.4.6
Free Energy per Spin
...............................266
6.4.7
Curie Temperature Tc
...............................267
6.4.8
Specific Heat
.....................................268
6.4.9
Spontaneous Magnetization
.........................269
6.5
Problems
.................................................270
References
......................................................271
7 Heisenberg
Model
...............................................273
7.1
Model Hamiltonian
........................................273
7.1.
1 Spin Operators
....................................273
7.1.2
Model Extensions
.................................279
7.2
Exact Statements
..........................................283
7.2.1
Mermin-Wagner Theorem
..........................283
7.2.2
One-Magnon States of a Ferromagnet
.................291
7.3
Molecular Field Approximations
.............................296
7.3.1
Ferromagnet
......................................297
7.3.2
Antiferromagnet
...................................303
7.3.3
Ferrimagnet
......................................317
7.4
Spin Waves
...............................................322
7.4.
1 Linear Spin Wave Theory for the
Isotropie
Ferromagnet
. 322
7.4.2
Renormalized Spin Waves
.........................329
7.4.3
Harmonic Approximation for Antiferromagnets
........336
7.4.4
Harmonic Approximation for a
Ferromagnet with Dipolar Interaction
.................345
Contents
7.5
Thermodynamics of
S
= 1 /2
Ferromagnet
.....................351
7.5.1
Tyablikov Decoupling
..............................35
1
7.5.2
Spontaneous Magnetization
.........................354
7.5.3
Thermodynamic Potentials
..........................359
7.6
Thermodynamics of
5 >
I
/2
Ferromagnets
....................361
7.6.1
Green s Functions
.................................361
7.6.2
Spontaneous Magnetization
.........................363
7.6.3
The
Callen
Method
................................371
7.7
Problems
.................................................381
References
......................................................386
Hubbard Model
................................................387
8.1
Introduction
..............................................387
8.2
Model for Band Magnets
...................................388
8.2.1
Solid as a Many-Body System
.......................388
8.2.2
Electrons in Narrow Energy Bands
...................389
8.2.3
Hubbard Model
...................................393
8.3
Stoner
Model
.............................................395
8.3.1
Stoner
Ansatz
(Ferromagnet)
........................395
8.3.2
Stoner
Excitations
.................................397
8.3.3
Magnetic Phase Transition
..........................398
8.3.4
Static Susceptibility
................................405
8.4
Exact Statements and General Properties
......................409
8.4.1
Mermin-Wagner Theorem
..........................410
8.4.2
The Infinitely Narrow Band
.........................415
8.4.3
The Two-Site Model
...............................420
8.4.4
The Exactly Half-Filled Band
........................427
8.4.5
Strong-Coupling Regime
...........................431
8.4.6
Spectra] Moments
.................................437
8.4.7
High-Energy Expansions
...........................439
8.4.8
Weak-Coupling Regime
............................441
8.4.9
Infinite Dimensions
................................444
8.4.10
Effective
impurity^Problem
........................448
8.5
Magnetism and Electronic Correlations
.......................451
8.5.1
Hubbard-I Approximation
..........................451
8.5.2
Interpolation Method
...............................454
8.5.3
Correlation Effects and Ferromagnetism
...............455
8.5.4
Criterion for Ferromagnetism
........................457
8.5.5
Static Susceptibility and Ferromagnetism
..............461
8.5.6
Spin-Dependent Band Shift
.........................464
8.5.7
Quasiparticle Damping
.............................470
8.5.8
Dynamical Mean Field Theory
.......................475
8.5.9
Modified Perturbation Theory
.......................479
Contents xiii
8.5.10 Curie
Temperature, Magnetization and Static
Susceptibility
.....................................482
8.6
Problems
.................................................485
References
......................................................490
A Second Quantization
............................................491
A.I Identical Particles
..........................................492
A.2 Continuous Fock Representation
.............................494
A.
2.1
Symmetrized Many-Particle States
...................494
A.
2.2
Construction Operators
.............................495
A.
2.3
Many-Body Operators
..............................497
A.3 Discrete Fock Representation (Occupation Number
Representation)
........................................... 501
A.3.1 Symmetrized Many-Particle States
...................501
A.
3.2
Construction Operators
.............................503
A.4 Examples
................................................506
A.4.1 Bloch Electrons
...................................506
A.4.2 Wannier Electrons
.................................508
A.4.3 Density Operator
..................................509
A.4.4 Coulomb Interaction
...............................510
A.5 Problems
.................................................511
В
The Method of Green s Functions
.................................515
B.
1
Linear Response Theory
....................................515
B.I.I
Kubo
Formula
....................................515
B.1.2 Magnetic Susceptibility
.............................518
B.
1.3
Dielectric Function
................................520
B.2 Spectroscopies and Spectral Densities
.........................523
B.3 Double-Time Green s Functions
.............................528
B.3.
1
Definitions and Equations of Motion
..................528
B.3.2 Spectral Representations
............................531
B.3.3 Spectral Theorem
..................................534
B.3.4 Spectral Moments
.................................536
B.3.5 Kramer s-Kronig Relations
.........................537
B.3.6 Simple Applications
...............................539
B.4 The Quasiparticle Concept
..................................545
B.4.
1
Interacting Electrons
...............................545
B.4.2 Electronic Self-energy
..............................548
B.4.3 Quasiparticles
.....................................551
B.4.4 Quasiparticle Density of States
......................555
B.4.5 Thermodynamics
..................................558
B.5 Problems
.................................................559
С
Solutions to Problems
...........................................563
Index
.............................................................743
|
| adam_txt |
Contents
1
Basic Facts
. 1
1.1
Macroscopic Maxwell Equations
. 1
1.2
Magnetic Moment and Magnetization
. 7
1.3
Susceptibility
. 13
1.4
Classification of Magnetic Materials
. 15
1.4.1
Diamagnetism
. 15
1
.4.2
Paramagnetism
. 15
1.4.3
Collective Magnetism
. 17
1.5
Elements of Thermodynamics
. 19
1.6
Problems
. 22
2
Atomic Magnetism
. 25
2.1
Hund's Rules
. 25
2.1.1
Russell-Saunders (LS-) Coupling
. 25
2.1.2
Hund's Rules for
¿5
Coupling
. 27
2.2
Dirac Equation
. 28
2.3
Electron Spin
. 34
2.4
Spin-Orbit Coupling
. 40
2.5
Wigner-Eckart Theorem
. 45
2.5.1
Rotation
. 45
2.5.2
Rotation Operator
. 47
2.5.3
Angular Momentum
. 48
2.5.4
Rotation Matrices
. 50
2.5.5
Tensor Operators
. 52
2.5.6
Wigner-Eckart Theorem
. 53
2.5.7
Examples of Application
. 55
2.6
Electron in an External Magnetic Field
. 56
2.7
Nuclear Quadrupole Field
. 62
2.8
Hyperfine Field
. 67
2.9
Magnetic Hamiitonian of the Atomic Electron
. 72
2.10
Many-Electron Systems
. 74
2.10.1
Coulomb Interaction
. 74
x
Contents
2.10.2
Spin-Orbit Coupling
. 75
2.10.3
Further Couplings
. 76
2.11
Problems
. 81
3
Diamagnetism
. 85
3.1
Bohr-van
Leeuwen
Theorem
. 85
3.2
Larmor Diamagnetism (Insulators)
. 87
3.3
The
Sommerfeld
Model of a Metal
. 90
3.3.1
Properties of the Model
. 91
3.3.2 Sommerfeld
Expansion
. 99
3.4
Landau Diamagnetism (Metals)
.104
3.4.1
Free Electrons in Magnetic Field (Landau Levels)
.104
3.4.2
Grand Canonical Potential of the Conduction Electrons
. 109
3.4.3
Susceptibility of the Conduction Electrons
.117
3.5
The
de Haas-Van Alphen
Effect
.121
3.5.1
Oscillations in the Magnetic Susceptibility
.121
3.5.2
Electron Orbits in Magnetic Field
.124
3.5.3
Physical Origin of the Oscillations
.128
3.5.4
Onsager Argument
.131
3.6
Problems
.134
References
.136
4
Paramagnetism
.137
4.1 Pauli
Spin Paramagnetism
.138
4.1.1
"Primitive" Theory of the
Pauli
Spin Paramagnetism
. 138
4.1.2
Temperature Corrections
.141
4.1.3
Exchange Corrections
.142
4.2
Paramagnetism of the Localized Electrons
.155
4.2.1
Weak Spin-Orbit Interaction
.158
4.2.2
Strong Spin-Orbit Coupling
.164
4.2.3
Van Vleck Paramagnetism
.166
4.3
Problems
.171
References
.174
5
Exchange Interaction
.175
5.1
Phenomenological Theories
.178
5.1.1
The Exchange Field
.178
5.1.2
Weiss Ferromagnet
.180
5.2
Direct Exchange Interaction
.184
5.2.1
Pauli's Principle
.184
5.2.2
The Heitler-London Method
.188
5.2.3
Dirac's Vector Model
.195
5.3
Indirect Exchange Interaction
.200
5.3.1
Rudermann-Khtel-Kasuya-Yosida (RKKY) Interaction
. 200
5.3.2
Superexchange
.209
Contents xi
5.3.3 Double Exchange.217
5.4 Problems.226
References
.231
6 Ising Model .233
6.1 The Model .234
6.2
The One Dimensional
Ising Model.236
6.2.
t
Spontaneous Magnetization
.236
6.2.2
One Dimensional Ising Model in External Field
.240
6.3
The Phase Transition of Two-Dimensional Ising Model
.245
6.3.1
The Method of Proof
.245
6.3.2
Finite Ising Lattice with Special Boundary Conditions
. 247
6.3.3
Probabilities
.247
6.3.4
Realization Possibilities for the Polygons
.249
6.3.5
Magnetization of the Finite Lattice
.252
6.3.6
Thermodynamic Limit
.252
6.4
The Free Energy of the Two-Dimensional Ising Model
.254
6.4.1
High-Temperature Expansion
.255
6.4.2
Spin Products as Graphs
.256
6.4.3
Loops
.257
6.4.4
Directed Paths
.261
6.4.5
Matrix Mt
.264
6.4.6
Free Energy per Spin
.266
6.4.7
Curie Temperature Tc
.267
6.4.8
Specific Heat
.268
6.4.9
Spontaneous Magnetization
.269
6.5
Problems
.270
References
.271
7 Heisenberg
Model
.273
7.1
Model Hamiltonian
.273
7.1.
1 Spin Operators
.273
7.1.2
Model Extensions
.279
7.2
Exact Statements
.283
7.2.1
Mermin-Wagner Theorem
.283
7.2.2
One-Magnon States of a Ferromagnet
.291
7.3
Molecular Field Approximations
.296
7.3.1
Ferromagnet
.297
7.3.2
Antiferromagnet
.303
7.3.3
Ferrimagnet
.317
7.4
Spin Waves
.322
7.4.
1 Linear Spin Wave Theory for the
Isotropie
Ferromagnet
. 322
7.4.2
"Renormalized" Spin Waves
.329
7.4.3
Harmonic Approximation for Antiferromagnets
.336
7.4.4
Harmonic Approximation for a
Ferromagnet with Dipolar Interaction
.345
Contents
7.5
Thermodynamics of
S
= 1 /2
Ferromagnet
.351
7.5.1
Tyablikov Decoupling
.35
1
7.5.2
Spontaneous Magnetization
.354
7.5.3
Thermodynamic Potentials
.359
7.6
Thermodynamics of
5 >
I
/2
Ferromagnets
.361
7.6.1
Green's Functions
.361
7.6.2
Spontaneous Magnetization
.363
7.6.3
The
Callen
Method
.371
7.7
Problems
.381
References
.386
Hubbard Model
.387
8.1
Introduction
.387
8.2
Model for Band Magnets
.388
8.2.1
Solid as a Many-Body System
.388
8.2.2
Electrons in Narrow Energy Bands
.389
8.2.3
Hubbard Model
.393
8.3
Stoner
Model
.395
8.3.1
Stoner
Ansatz
(Ferromagnet)
.395
8.3.2
Stoner
Excitations
.397
8.3.3
Magnetic Phase Transition
.398
8.3.4
Static Susceptibility
.405
8.4
Exact Statements and General Properties
.409
8.4.1
Mermin-Wagner Theorem
.410
8.4.2
The Infinitely Narrow Band
.415
8.4.3
The Two-Site Model
.420
8.4.4
The Exactly Half-Filled Band
.427
8.4.5
Strong-Coupling Regime
.431
8.4.6
Spectra] Moments
.437
8.4.7
High-Energy Expansions
.439
8.4.8
Weak-Coupling Regime
.441
8.4.9
Infinite Dimensions
.444
8.4.10
Effective
"impurity^Problem
.448
8.5
Magnetism and Electronic Correlations
.451
8.5.1
Hubbard-I Approximation
.451
8.5.2
Interpolation Method
.454
8.5.3
Correlation Effects and Ferromagnetism
.455
8.5.4
Criterion for Ferromagnetism
.457
8.5.5
Static Susceptibility and Ferromagnetism
.461
8.5.6
Spin-Dependent Band Shift
.464
8.5.7
Quasiparticle Damping
.470
8.5.8
Dynamical Mean Field Theory
.475
8.5.9
Modified Perturbation Theory
.479
Contents xiii
8.5.10 Curie
Temperature, Magnetization and Static
Susceptibility
.482
8.6
Problems
.485
References
.490
A Second Quantization
.491
A.I Identical Particles
.492
A.2 Continuous Fock Representation
.494
A.
2.1
Symmetrized Many-Particle States
.494
A.
2.2
Construction Operators
.495
A.
2.3
Many-Body Operators
.497
A.3 Discrete Fock Representation (Occupation Number
Representation)
. 501
A.3.1 Symmetrized Many-Particle States
.501
A.
3.2
Construction Operators
.503
A.4 Examples
.506
A.4.1 Bloch Electrons
.506
A.4.2 Wannier Electrons
.508
A.4.3 Density Operator
.509
A.4.4 Coulomb Interaction
.510
A.5 Problems
.511
В
The Method of Green's Functions
.515
B.
1
Linear Response Theory
.515
B.I.I
Kubo
Formula
.515
B.1.2 Magnetic Susceptibility
.518
B.
1.3
Dielectric Function
.520
B.2 Spectroscopies and Spectral Densities
.523
B.3 Double-Time Green's Functions
.528
B.3.
1
Definitions and Equations of Motion
.528
B.3.2 Spectral Representations
.531
B.3.3 Spectral Theorem
.534
B.3.4 Spectral Moments
.536
B.3.5 Kramer's-Kronig Relations
.537
B.3.6 Simple Applications
.539
B.4 The Quasiparticle Concept
.545
B.4.
1
Interacting Electrons
.545
B.4.2 Electronic Self-energy
.548
B.4.3 Quasiparticles
.551
B.4.4 Quasiparticle Density of States
.555
B.4.5 Thermodynamics
.558
B.5 Problems
.559
С
Solutions to Problems
.563
Index
.743 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Nolting, Wolfgang 1944- Ramakanth, Anupuru |
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| bvnumber | BV035122294 |
| callnumber-first | Q - Science |
| callnumber-label | QC754 |
| callnumber-raw | QC754.2.Q34 |
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| classification_rvk | UP 6000 |
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| ctrlnum | (OCoLC)243822187 (DE-599)HBZHT015663364 |
| dewey-full | 538.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 538 - Magnetism |
| dewey-raw | 538.4 |
| dewey-search | 538.4 |
| dewey-sort | 3538.4 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| discipline_str_mv | Physik |
| format | Book |
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| id | DE-604.BV035122294 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:21:39Z |
| indexdate | 2024-07-09T21:22:49Z |
| institution | BVB |
| isbn | 9783540854159 9783540854166 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016789931 |
| oclc_num | 243822187 |
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| physical | XIII, 752 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
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| publisher | Springer |
| record_format | marc |
| spelling | Nolting, Wolfgang 1944- Verfasser (DE-588)115505261 aut Quantum theory of magnetism Wolfgang Nolting and Anupuru Ramakanth Heidelberg [u.a.] Springer 2009 XIII, 752 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Quantentheorie Magnetism Quantum theory Quantentheorie (DE-588)4047992-4 gnd rswk-swf Magnetismus (DE-588)4037021-5 gnd rswk-swf Magnetismus (DE-588)4037021-5 s Quantentheorie (DE-588)4047992-4 s DE-604 Ramakanth, Anupuru Verfasser aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016789931&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nolting, Wolfgang 1944- Ramakanth, Anupuru Quantum theory of magnetism Quantentheorie Magnetism Quantum theory Quantentheorie (DE-588)4047992-4 gnd Magnetismus (DE-588)4037021-5 gnd |
| subject_GND | (DE-588)4047992-4 (DE-588)4037021-5 |
| title | Quantum theory of magnetism |
| title_auth | Quantum theory of magnetism |
| title_exact_search | Quantum theory of magnetism |
| title_exact_search_txtP | Quantum theory of magnetism |
| title_full | Quantum theory of magnetism Wolfgang Nolting and Anupuru Ramakanth |
| title_fullStr | Quantum theory of magnetism Wolfgang Nolting and Anupuru Ramakanth |
| title_full_unstemmed | Quantum theory of magnetism Wolfgang Nolting and Anupuru Ramakanth |
| title_short | Quantum theory of magnetism |
| title_sort | quantum theory of magnetism |
| topic | Quantentheorie Magnetism Quantum theory Quantentheorie (DE-588)4047992-4 gnd Magnetismus (DE-588)4037021-5 gnd |
| topic_facet | Quantentheorie Magnetism Quantum theory Magnetismus |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016789931&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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