Statistical MechanicsUnlike most other texts on the subject, this clear, concise introduction to the theory of microscopic bodies treats the modern theory of critical phenomena. Provides up-to-date coverage of recent major advances, including a self-contained description of thermodynamics and the classical kinetic theory of gases, interesting applications such as superfluids and the quantum Hall effect, several current research applications, The last three chapters are devoted to the Landau-Wilson approach to critical phenomena. Many new problems and illustrations have been added to this edition. |
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Page 364
... cosh 2 cosh 24 cosh 20 sinh 20 —i cosh 2 sinh 20 ( 17.91 ) cosh 24 cosh 20 - } sinh 2 sinh 20 i sinh 2 ¢ sinh ” B = ( 17.92 ) −i sinh 26 cosh® 0 − } sinh 2 sinh 20 and B is the hermitian conjugate of B. To find the eigenvalues of w ...
... cosh 2 cosh 24 cosh 20 sinh 20 —i cosh 2 sinh 20 ( 17.91 ) cosh 24 cosh 20 - } sinh 2 sinh 20 i sinh 2 ¢ sinh ” B = ( 17.92 ) −i sinh 26 cosh® 0 − } sinh 2 sinh 20 and B is the hermitian conjugate of B. To find the eigenvalues of w ...
Page 365
... cosh Y ( 17.102 ) ( 17.103 ) Evaluating the trace with the help of ( 17.91 ) , ( 17.92 ) , and ( 17.99 ) we obtain πk cosh = Yk - cosh 24 cosh 20 COS sinh 2 ¢ sinh 20 n ( k = 0 , 1 , ... , 2n - 1 ) ( 17.104 ) is also a solution . But ...
... cosh Y ( 17.102 ) ( 17.103 ) Evaluating the trace with the help of ( 17.91 ) , ( 17.92 ) , and ( 17.99 ) we obtain πk cosh = Yk - cosh 24 cosh 20 COS sinh 2 ¢ sinh 20 n ( k = 0 , 1 , ... , 2n - 1 ) ( 17.104 ) is also a solution . But ...
Page 368
... cosh y ( v ) = cosh 24 cosh 20 - cos v sinh 24 sinh 20 ( 17.121 ) with Φ = βε , ε > 0 0 = tanh -1 -24 e ( 17.122 ) A straightforward calculation shows that 1 sinh 20 = sinh 368 Special Topics in Statistical Mechanics.
... cosh y ( v ) = cosh 24 cosh 20 - cos v sinh 24 sinh 20 ( 17.121 ) with Φ = βε , ε > 0 0 = tanh -1 -24 e ( 17.122 ) A straightforward calculation shows that 1 sinh 20 = sinh 368 Special Topics in Statistical Mechanics.
Contents
THE LAWS OF THERMODYNAMICS | 3 |
SOME APPLICATIONS OF THERMODYNAMICS | 33 |
THE PROBLEM OF KINETIC THEORY | 55 |
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absolute zero approximation assume assumption atoms average becomes Boltzmann Bose calculate called canonical ensemble classical collision complete condition consider constant contains coordinates corresponds defined definition denoted density depends derivation determined discussion distribution effect eigenvalues elements energy ensemble entropy equal equation equilibrium excited exists expansion external fact Fermi field finite given ground Hamiltonian heat Hence ideal independent integral interaction lattice levels limit liquid magnetic mass matrix mean molecular molecules momentum n₁ obtain occupation operator particles partition function phase physical positive possible potential pressure probability problem properties quantity quantum quantum mechanics region represented respectively result satisfies shown in Fig solution specific statistical mechanics temperature theorem theory thermodynamic transformation transition unit V₁ V₂ valid volume wave function