Preface
PART I QUANTUM STATISTICAL MECHANICS
CHAPTER 1 THE LIOUVILLE EQUATION IN CLASSICAL MECHANICS
1.Introduction: Statistical approach in classical and quantum mechanics
2.The classical statistical approach
a) A transformation operator G
b) Probability density D
c) The Liouville theorem
d) Time dependent probability density Dt, to
3.Quantum analogy
4.Symmetry properties
5.Isolated dynamical systems
6.A system of identical monoatomic molecules
7.Property of reversibility
CHAPTER 2 THE LIOUVILLE EQUATION IN QUANTUM MECHANICS
1.The X-representation
2.Quantum statistical approach
a) Statistical operators
b) The Liouville equation
c) Operator Ut, to
d) Properties of the statistical operators
3.Symmetry properties
4.Discrete X-representation
5.Discrete momentum representation
6.Compatibility with the Schroedinger equation
7.Limit transition and cyclic boundary condition
8.An isolated dynamical system
9.Conservation and non-conservation of particle number
a) N-particle wave functions
b) X-representation for variable particle numbers
c) The Hilbert space of wave functions and its subspaces
d) A projection operator
e) A combined index
CHAPTER 3 CANONICAL DISTRIBUTION AND THERMODYNAMIC FUNCTIONS
1.Integrals of motion
2.The Gibbs canonical distribution
3.Thermodynamic functions
4.Quasi-static processes
a) The concept of quasi-static process
b) Construction of quasi-static processes
c) Interpretation of terms
d) Heat capacity
e) Homogeneous systems
f) Relation between H and E
5.Passing to limits
a) Basic assumptions
b) Boundary surface
c) Limits
d) Validity of speculations on passing to limits
6.The grand canonical ensemble
a) Statistical operators
b) Definitions of μ, Γ and G
c) Uniqueness of μj
PART II SOME ASPECTS OF THE METHOD OF SECONDARY QUANTIZATION
PART III QUADRATIC HAMILTONIANS AND THEIR APPLICATION
PART IV SUPERFLUIDITY AND QUASI-AVERAGES IN PROBLEMS OF STATISTICAL MECHANICS
Photos
Index
