Statistical Mechanics - Physics at Oregon State University

More documents

Recommendations

Info

138 CHAPTER 6. DENSITY MATRIX FORMALISM. (A) How many eigenvalues of ρ are equal to 1? (B) What is the entropy of the system? (C) Assume that the particles are independent. If a single particle is described by a density operator ρi, how do you construct ρ from the ρi?
Chapter 7 Classical statistical mechanics. 7.1 Relation between quantum and classical mechanics. Choice of basis. Based on the knowledge of quantum statistical mechanics, it is straightforward to derive the expressions valid for a classical description of a many particle system. A classical state of a system is defined by the values of the positions ri and momenta pi. These vectors are combined in a single vector X in a 6Ndimensional phase-space. Every value of X corresponds to a certain state of the system. The classical Hamiltonian H( X) is constructed from the quantum mechanical one by replacing momentum operators by numbers pi. A good basis for the expressions for the density matrix is therefore the set of all vectors | X >. In quantum mechanics it is impossible to specify both the position and the momentum of a particle at the same time, since the position and momentum operators do not commute. The commutators are proportional to and one way of thinking about the classical limit of quantum mechanics is to assume that → 0. In this sense the position and momentum operators do commute in the classical limit and we are allowed to use their simultaneous eigenvalues as labels characterizing the state of a system. Wigner distribution function. In a more formal approach we use so-called Wigner distribution functions, defined by 139
Page 1:
Statistical Mechanics Henri J.F. Ja
Page 4 and 5:
IV CONTENTS 4.3 Gas of poly-atomic
Page 6 and 7:
VI CONTENTS
Page 8 and 9:
VIII INTRODUCTION Introduction. The
Page 10 and 11:
X INTRODUCTION In chapter nine we d
Page 12 and 13:
2 CHAPTER 1. FOUNDATION OF STATISTI
Page 14 and 15:
Page 16 and 17:
Page 18 and 19:
Page 20 and 21:
10 CHAPTER 1. FOUNDATION OF STATIST
Page 22 and 23:
Page 24 and 25:
Page 26 and 27:
Page 28 and 29:
Page 30 and 31:
Page 32 and 33:
Page 34 and 35:
24 CHAPTER 2. THE CANONICAL ENSEMBL
Page 36 and 37:
Page 38 and 39:
Page 40 and 41:
Page 42 and 43:
Page 44 and 45:
Page 46 and 47:
Page 48 and 49:
Page 50 and 51:
Page 52 and 53:
Page 54 and 55:
44 CHAPTER 3. VARIABLE NUMBER OF PA
Page 56 and 57:
Page 58 and 59:
Page 60 and 61:
Page 62 and 63:
Page 64 and 65:
Page 66 and 67:
Page 68 and 69:
Page 70 and 71:
Page 72 and 73:
Page 74 and 75:
Page 76 and 77:
Page 78 and 79:
68 CHAPTER 4. STATISTICS OF INDEPEN
Page 80 and 81:
Page 82 and 83:
Page 84 and 85:
Page 86 and 87:
Page 88 and 89:
Page 90 and 91:
Page 92 and 93:
Page 94 and 95:
Page 96 and 97:
Page 98 and 99: 88 CHAPTER 4. STATISTICS OF INDEPEN
Page 100 and 101: 90 CHAPTER 5. FERMIONS AND BOSONS
Page 102 and 103: 92 CHAPTER 5. FERMIONS AND BOSONS t
Page 104 and 105: 94 CHAPTER 5. FERMIONS AND BOSONS w
Page 106 and 107: 96 CHAPTER 5. FERMIONS AND BOSONS T
Page 108 and 109: 98 CHAPTER 5. FERMIONS AND BOSONS S
Page 130 and 131: 120 CHAPTER 6. DENSITY MATRIX FORMA
Page 150 and 151: 140 CHAPTER 7. CLASSICAL STATISTICA
Page 168 and 169: 158 CHAPTER 8. MEAN FIELD THEORY: C
Page 198 and 199:
188 CHAPTER 8. MEAN FIELD THEORY: C
Page 200 and 201:
190 CHAPTER 8. MEAN FIELD THEORY: C
Page 202 and 203:
192 CHAPTER 9. GENERAL METHODS: CRI
Page 204 and 205:
Page 206 and 207:
Page 208 and 209:
Page 210 and 211:
Page 212 and 213:
Page 214 and 215:
Page 216 and 217:
Page 218 and 219:
Page 220 and 221:
Page 222 and 223:
Page 224 and 225:
Page 226 and 227:
Page 228 and 229:
Page 230 and 231:
Page 232 and 233:
Page 234 and 235:
Page 236 and 237:
Page 238 and 239:
Page 240 and 241:
230 APPENDIX A. SOLUTIONS TO SELECT
Page 242 and 243:
Page 244 and 245:
Page 246 and 247:
Page 248 and 249:
Page 250 and 251:
Page 252 and 253:
Page 254 and 255:
Page 256 and 257:
Page 258 and 259:
Page 260 and 261:
Page 262 and 263:
Page 264 and 265:
Page 266 and 267:
Page 268 and 269:
Page 270:
show all

Statistical Mechanics - Physics at Oregon State University

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?