Statistical Mechanics - Physics at Oregon State University

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254 APPENDIX A. SOLUTIONS TO SELECTED PROBLEMS. n(1 + nλ 3 5 − T 2 2 ) ≈ 2λ −3 T λ λ ≈ n 1 2 λ3T (1 + nλ 3 5 − T 2 2 ) Inserting in the pressure, and only keeping terms to second order: p ≈ 2kBT λ −3 5 T λ(1 − λ2− 2 ) p ≈ 2kBT λ −3 T n1 2 λ3T (1 + nλ 3 5 − T 2 2 )(1 − n 1 2 λ3 5 − T 2 2 ) p ≈ kBT n(1 + nλ 3 5 − T 2 2 − n 1 2 λ3 5 − T 2 2 ) B2(T ) = λ 3 7 − T 2 2 This is positive, increasing the pressure, due to the fact that fermions do not like to be in the same place. Solution Problem 6. The chemical potential follows from the equation for N: N = fF D(ɛo; T, µ) which is in this case N = 2V (2π) 3 o d 3 kfF D( 2 c 2 k 2 + m 2 c 4 ; T, µ) and there are no convergence problems, like in the notes. This gives N = 2V (2π) 3 d 3 1 k eβ(√2c2 k2 +m2c4−µ) + 1 with β = 1 kBT and The equation for N gives . At T = 0 this reduces to N = 2V (2π) 3 ɛF = k
A.5. SOLUTIONS FOR CHAPTER 5. 255 or kF = 3π 2 N V The internal energy at T = 0 follows from a similar expression: U(T = 0) = 2V (2π) 3 d 3 k 2c2k2 + m2c4 or k
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Statistical Mechanics Henri J.F. Ja
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IV CONTENTS 4.3 Gas of poly-atomic
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VI CONTENTS
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VIII INTRODUCTION Introduction. The
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X INTRODUCTION In chapter nine we d
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2 CHAPTER 1. FOUNDATION OF STATISTI
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10 CHAPTER 1. FOUNDATION OF STATIST
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44 CHAPTER 3. VARIABLE NUMBER OF PA
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68 CHAPTER 4. STATISTICS OF INDEPEN
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90 CHAPTER 5. FERMIONS AND BOSONS
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92 CHAPTER 5. FERMIONS AND BOSONS t
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94 CHAPTER 5. FERMIONS AND BOSONS w
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96 CHAPTER 5. FERMIONS AND BOSONS T
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120 CHAPTER 6. DENSITY MATRIX FORMA
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140 CHAPTER 7. CLASSICAL STATISTICA
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158 CHAPTER 8. MEAN FIELD THEORY: C
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192 CHAPTER 9. GENERAL METHODS: CRI
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Statistical Mechanics - Physics at Oregon State University

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