Thermodynamics, Statistical Physics, and Quantum Mechanics

36 PROBLEMS a)Derive the average number of photons in the box. Hint: b) c) d) e) What is the total energy of the radiation in th ...

THERMODYNAMICS AND STATISTICAL PHYSICS 37 a) Show that the isothermal work done by the gas is b) where is the average number of ...

38 PROBLEMS 4.79 Dark Matter (Rutgers) Fromvirial theorem arguments, thevelocity dispersions ofbrightstars in dwarf elliptical g ...

THERMODYNAMICS AND STATISTICAL PHYSICS 39 4.80 Einstein Coefficients (Stony Brook) You have two-state atoms in a thermal radiati ...

40 PROBLEMS Determine the thermodynamic mean value of the magnetic moment and the magnetization of thesystemM, and calculate it ...

THERMODYNAMICS AND STATISTICAL PHYSICS 41 Derive expressions for the Partitionfunction Average spin Internalenergy 4.85 N Indepe ...

42 PROBLEMS where B is an external field, is the magnetic moment, and the prime indicates that the summation is only over the ne ...

THERMODYNAMICS AND STATISTICAL PHYSICS 43 4.90 Gas Fluctuations (Moscow Phys-Tech) A high-vacuum chamber is evacuated to a press ...

44 PROBLEMS b)From (a), find the relation between and the meansquare fluctua- tion of N in the grand canonical ensemble. How doe ...

THERMODYNAMICS AND STATISTICAL PHYSICS 45 Applications to Solid State 4.97 Thermal Expansion and Heat Capacity (Princeton) a) Fi ...

46 PROBLEMS becomes animperfectcrystalwith defects (of the Frenkeltype). The number of interstitial sites into which an atom can ...

THERMODYNAMICS AND STATISTICAL PHYSICS 47 d)Find the low-temperature limit of the heat capacity and explain why it is reasonable ...

48 PROBLEMS 4.105 Adiabatic Demagnetization (Maryland) A paramagnetic sample is subjected to magnetic cooling. a) Show that Assu ...

THERMODYNAMICS AND STATISTICAL PHYSICS 49 For an adiabatic process, show that the ratio of final and initial tem- peratures is g ...

This page intentionally left blank ...

5 Quantum Mechanics One-Dimensional Potentials 5.1 Shallow Square Well I (Columbia) A particle ofmass moving in onedimension has ...

52 PROBLEMS 5.2 Shallow Square Well II (Stony Brook) A particle of mass is confined tomove in onedimension by a potential (seeFi ...

53 is Find the eigenvalue andeigenfunction ofthe boundstate. If the system is in thebound state and the strength of thepotential ...

54 PROBLEMS 5.5 Two Delta Function Potentials (Rutgers) A particle ofmass moves in aone-dimensionalpotential of theform where P ...

55 function is at thecenter of the box. a) b) c) What are theeigenvalues ofodd-paritystates? Find the value ofCfor which thelowe ...