Statistical mechanics for beginners: a textbook for undergraduates
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
2010
|
| Subjects: | |
| Online Access: | Klappentext Inhaltsverzeichnis |
| Physical Description: | 162 S. |
| ISBN: | 9789814299121 9789814299114 |
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MARC
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| 245 | 1 | 0 | |a Statistical mechanics for beginners |b a textbook for undergraduates |
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Record in the Search Index
| _version_ | 1804143362541879297 |
|---|---|
| adam_text | Contents
Dedication
v
Preface
vii
List of Figures
xiii
Physical Constants
xv
Introduction
1
I. Fundamentals
7
1.
The Closed System or the Microcanonicai Ensemble
9
1.1
The Microcanonicai Ensemble
............. 9
1.2
Properties of the Entropy
............... 12
1.3
An Example
....................... 17
2.
The System in Thermal Contact with a Reservoir:
The Canonical and Grand Canonical Ensembles
22
2.1
The Canonical Ensemble
................ 23
2.1.1
The partition function
.............. 23
χ
Statistical Mechanics for Beginners
2.1.2
Energy, entropy and thermodynamic
potential
..................... 26
2.1.3
A two-level system
................ 29
2.1.4
The ideal gas; equipartition of energy
in classical mechanics
.............. 30
2.2
The Grand Canonical Ensemble
............ 33
2.2.1
The grand partition function
.......... 34
2.2.2
The number of particles, energy, entropy and
the grand potential
............... 36
2.2.3
An example
................... 38
2.3
Summary
........................ 41
2.3.1
Fluctuations
................... 42
2.3.2
Final remark
................... 43
3.
Quantum Statistics
44
3.1
The Partition Function and the Free Energy
..... 45
3.1.1
For variable
N
and for
fermions
........ 46
3.1.2
For variable
N
and for bosons
......... 46
3.1.3
For fixed N, and for both
fermions
and bosons
.................... 47
3.2
The Energy and the Entropy
.............. 49
3.3
The Classical Ideal Gas: Maxwell-Boltzmann
Statistics
......................... 50
3.4
Qualitative Behavior of the Chemical Potential and
the Derivation of
(θμ/οΤ)νίΝ
< 0........... 53
3.4.1
Bosons
...................... 53
3.4.2
Fermions
..................... 54
4.
The Density of States
55
4.1
The Wave Vector
.................... 56
4.2
The Density of States
.................. 57
4.3
The Monatomic Ideal Gas
............... 58
4.3.1
The partition function
.............. 58
4.3.2
The internal energy, entropy and equation of
state
....................... 59
4.3.3
The classical limit
................ 60
Contents xi
5.
Some
Problems 61
5.1 The Quantum
Harmonic Oscillator
.......... 61
5.1.1
Low temperature limit
............. 64
5.1.2
High temperature limit
............. 65
5.2
The Polyatomic Ideal Gas
............... 66
5.3
Bosons and
Fermions
in a Two-Level System
..... 68
5.3.1
The particles are bosons
............ 69
5.3.2
The particles are
fermions
........... 72
5.3.3
Classical particles
................ 73
5.4
The Magnetic Chain
.................. 75
II. Applications
79
6.
The Gas of Photons: The Black Body Radiation
81
6.1
The Energy and the Energy Spectrum
........ 83
6.2
The Free Energy and the Entropy
........... 87
6.2.1
The relation with the wave picture
....... 88
6.3
Light Emission and Absorption of Solids;
Kirchhoff s Law
..................... 88
6.4
The Black Body Emission
............... 90
6.5
The Properties of Photon Gas are Independent
of the Shape and the Material of the Cavity
..... 90
7.
Atomic Vibration in Solids: Phonons
92
7.1
Atomic Vibration in Solids
............... 92
7.2
The Properties of Phonons
............... 97
7.3
The Low Temperature Case
.............. 97
7.4
The High Temperature Case
.............. 99
7.5
The Debye Formula
................... 100
7.6
Resolution of the Differential Equation
(7.1)
by
Means of Trigonometric Functions
........... 104
7.7
Derivation of the Expression
(7.30)
Giving
Су
in the
Debye Model
...................... 105
xii
Statistical Mechanics for Beginners
8.
The Boson Gas at Low Temperature:
The Bose-Einstein Condensation
107
8.1
The Chemical Potential
................108
8.2
The Energy, Specific Heat, Free Energy
and Entropy
.......................112
8.3
Experimental Verfication
................114
9.
The Gas of
Fermions:
Electrons in Metals and in
Semiconductors
116
9.1
Free Electrons in a Box
.................116
9.1.1
The Fermi-Dirac function
...........116
9.1.2
The chemical potential or
the Fermi level
.................. 120
9.1.3
The energy
.................... 123
9.1.4
The specifc heat
................. 127
9.1.5
Applications to metals
............. 129
9.2
Electrons in Semiconductors
.............. 131
10.
A History of Statistical Mechanics
136
10.1
Thermodynamics and Statistical Mechanics
Before Maxwell and Bolztmann
............ 136
10.2
The Kinetic Theory of Maxwell
............ 138
10.3
Boltzmann and Irreversibility
............. 139
10.4
Gibbs, the Father of Statistical Mechanics
...... 141
10.5
Planck and Einstein: Quantum Theory
and Statistics
......................142
10.6
The Method of
Bose
and the Bose-Einstein
Condensation
......................145
10.7
The Principle of
Pauli
and the Statistics
of Fermi and Dirac
...................146
10.8
Modern Developments
.................147
Exercises
148
Index
161
This textbook is for undergraduate students on a basic course in
Statistical Mechanics. The prerequisite is thermodynamics. It begins
with a study of three situations
—
the closed system and the systems
in thermal contact with a reservoir
—
in order, to formulate the
important fundamentals: entropy from Boltzmann formula, partition
function and grand partition function. Through the presentation of
quantum statistics,
Bose
statistics and Fermi-Dirac statistics are
established, including as a special case the classical situation of
Maxell-Boltzmann statistics. A series of examples ensue it: the
harmonic oscillator, the polymer chain, the two level system, bosons
(photons, phonons, and the Bose-Einstein condensation) and
fermions
(electrons in metals and in semiconductors). A compact historical
note on influential scientists forms the concluding chapter.
The unique presentation starts off with the principles, elucidating
the
weîl-developed
theory, and only thereafter the application of
theory. Calculations on the main steps are detailed, leaving behind
minimal gap. The author emphasizes with theory the link between
the macroscopic world (thermodynamics) and the microscopic world.
|
| any_adam_object | 1 |
| author | Benguigui, Lucien 1936- |
| author_GND | (DE-588)140061061 |
| author_facet | Benguigui, Lucien 1936- |
| author_role | aut |
| author_sort | Benguigui, Lucien 1936- |
| author_variant | l b lb |
| building | Verbundindex |
| bvnumber | BV036716184 |
| classification_rvk | UG 3100 |
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| ctrlnum | (OCoLC)699900717 (DE-599)BVBBV036716184 |
| discipline | Physik |
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| genre_facet | Einführung |
| id | DE-604.BV036716184 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:46:27Z |
| institution | BVB |
| isbn | 9789814299121 9789814299114 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020634163 |
| oclc_num | 699900717 |
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| physical | 162 S. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Benguigui, Lucien 1936- Verfasser (DE-588)140061061 aut Statistical mechanics for beginners a textbook for undergraduates Singapore [u.a.] World Scientific 2010 162 S. txt rdacontent n rdamedia nc rdacarrier Statistische Mechanik (DE-588)4056999-8 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Statistische Mechanik (DE-588)4056999-8 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020634163&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Klappentext Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020634163&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Benguigui, Lucien 1936- Statistical mechanics for beginners a textbook for undergraduates Statistische Mechanik (DE-588)4056999-8 gnd |
| subject_GND | (DE-588)4056999-8 (DE-588)4151278-9 |
| title | Statistical mechanics for beginners a textbook for undergraduates |
| title_auth | Statistical mechanics for beginners a textbook for undergraduates |
| title_exact_search | Statistical mechanics for beginners a textbook for undergraduates |
| title_full | Statistical mechanics for beginners a textbook for undergraduates |
| title_fullStr | Statistical mechanics for beginners a textbook for undergraduates |
| title_full_unstemmed | Statistical mechanics for beginners a textbook for undergraduates |
| title_short | Statistical mechanics for beginners |
| title_sort | statistical mechanics for beginners a textbook for undergraduates |
| title_sub | a textbook for undergraduates |
| topic | Statistische Mechanik (DE-588)4056999-8 gnd |
| topic_facet | Statistische Mechanik Einführung |
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