Basics of statistical physics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
2013
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 223 - 227 |
| Beschreibung: | XII, 233 S. graph. Darst. |
| ISBN: | 9789814449533 |
Internformat
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| 245 | 1 | 0 | |a Basics of statistical physics |c Harald J. W. Müller-Kirsten |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2013 | |
| 300 | |a XII, 233 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverz. S. 223 - 227 | ||
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Datensatz im Suchindex
| _version_ | 1804150707717144576 |
|---|---|
| adam_text | Titel: Basics of statistical physics
Autor: Müller-Kirsten, Harald J. W
Jahr: 2013
Contents
Preface to Second Edition ix
Preface to First Edition xi
1 Introduction 1
1.1 Introductory Remarks............................................1
1.2 Thermodynamic Potentials ......................................2
1.3 Capacity of Heat..................................................6
1.4 Frequently Used Terms............................................7
1.5 Applications and Examples......................................8
1.6 Problems without Worked Solutions............................9
2 Statistical Mechanics of an Ideal Gas (Maxwell) 11
2.1 Introductory Remarks............................................11
2.2 Maxwell s Treatment..............................................11
2.3 Lagrange s Method of Multipliers................................14
2.4 Applications........................................................17
2.4.1 Pressure exerted on the wall of a vessel ................17
2.4.2 Effusion of gas through a hole............................18
2.4.3 Thermionic emission......................................19
2.5 Distribution Function for all Directions ........................20
2.6 Applications and Examples......................................21
2.7 Problems without Worked Solutions............................24
3 The a priori Probability 27
3.1 Introductory Remarks............................................27
3.2 The a priori Probability..........................................27
3.3 Examples Illustrating Liouville s Theorem......................30
3.4 Insertion of Physical Conditions..................................31
3.5 Applications and Examples......................................35
3.6 Problems without Worked Solutions............................37
v
vi Contents
4 Classical Statistics (Maxwell—Boltzmann) 39
4.1 Introductory Remarks............................................39
4.2 The Number of Arrangements of Elements in
Maxwell-Boltzmann Statistics....................................39
4.3 Method of Maximum Probability................................41
4.3.1 The case of nonconserved elements......................43
4.3.2 The case of conserved elements..........................43
4.3.3 The meaning of /x ........................................44
4.3.4 Identification of /1 with 1/kT............................45
4.3.5 Distribution of particles in the atmosphere ............47
4.3.6 Law of equipartition of energy ..........................47
4.4 Applications........................................................48
4.4.1 The monatomic gas ......................................48
4.4.2 A solid......................................................49
4.5 Applications and Examples......................................49
4.6 Problems without Worked Solutions............................54
5 Entropy 57
5.1 Introductory Remarks............................................57
5.2 The Boltzmann Formula..........................................57
5.3 Applications and Examples......................................61
5.4 Problems without Worked Solutions............................66
6 Quantum Statistics 67
6.1 Introductory Remarks............................................67
6.2 A priori Weighting in Quantum Statistics......................68
6.2.1 Approximate calculation of number of states ..........71
6.2.2 Accurate calculation of number of states................72
6.2.3 Examples....................................................75
6.3 The Allowed Number of Elements in Quantum States .... 78
6.3.1 One element ..............................................78
6.3.2 Two non-interacting elements............................78
6.3.3 More than two elements stuck together ................80
6.4 Counting of Number of Arrangements..........................80
6.4.1 Fermi-Dirac statistics....................................80
6.4.2 Bose-Einstein statistics..................................82
6.5 Quantum Statistics at High Temperatures......................82
6.6 Applications........................................................84
6.7 Summary..........................................................85
6.8 Applications and Examples......................................86
6.9 Problems without Worked Solutions............................93
Contents vii
7 Exact Form of Distribution Functions 95
7.1 Introductory Remarks............................................95
7.2 Fermi-Dirac Occupation Numbers..............................95
7.3 Bose-Einstein Occupation Numbers ............................97
7.4 Thermodynamical Functions...................100
7.5 Applications and Examples...................100
7.6 Problems without Worked Solutions..............106
8 Application to Radiation (Light Quanta) 107
8.1 Introductory Remarks......................107
8.2 Planck s Radiation Law.....................108
8.3 Applications and Examples...................110
8.4 Problems without Worked Solutions..............115
9 Debye Theory of Specific Heat of Solids 119
9.1 Introductory Remarks......................119
9.2 The Calculation..........................121
9.3 Applications and Examples...................124
9.4 Problems without Worked Solutions..............129
10 Electrons in Metals 131
10.1 Introductory Remarks......................131
10.2 Evaluation of the Distribution Function............132
10.2.1 First approximation...................133
10.2.2 Second degree of approximation.............134
10.3 Applications and Examples...................136
10.4 Problems without Worked Solutions..............146
11 Limitations of the Preceding Theory — Improvement
with Ensemble Method 149
11.1 Introductory Remarks......................149
11.2 Ensembles — Three Types ...................152
11.2.1 Ensembles and ergodic hypothesis...........152
11.2.2 The ensemble distribution function...........154
11.3 The Canonical Ensemble of a Closed System .........156
11.3.1 Thermodynamics of a closed system..........157
11.4 The Grand Canonical Ensemble.................159
11.5 Ensemble Method of Maximum Probability..........160
11.6 Comments on the Function p..................161
11.7 Applications and Examples...................163
11.8 Problems without Worked Solutions..............168
viii
Contents
12 Averaging instead of Maximization, and Bose-Einstein
Condensation 169
12.1 Introductory Remarks......................169
12.2 The Darwin-Fowler Method of Mean Values..........170
12.2.1 Mean occupation number nj...............171
12.2.2 Taking subsidiary condition into account........172
12.3 Classical Statistics........................173
12.4 Quantum Statistics........................175
12.4.1 Fermi-Dirac statistics..................175
12.4.2 Bose-Einstein statistics.................176
12.4.3 Evaluation of the coefficient of u;N in .......176
12.5 Bose-Einstein Condensation...................182
12.5.1 The phenomenon of Bose-Einstein condensation . . . 182
12.5.2 Derivation of the Bose-Einstein distribution function
under condensation conditions .............183
12.6 Applications and Examples...................193
12.7 Problems without Worked Solutions..............204
13 The Boltzmann Transport Equation 207
13.1 Introductory Remarks......................207
13.2 Distribution Functions......................207
13.3 Solution of the Boltzmann Equation..............209
13.3.1 Solving the Boltzmann equation for two typical cases . 210
13.3.2 Calculation of the current density ...........211
13.3.3 Application to metals..................212
13.3.4 Calculation of the relaxation time ...........214
13.4 Applications and Examples...................220
13.5 Problems without Worked Solutions..............220
Bibliography 223
Index
229
|
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