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Imagine a certain kind of particle, such that each single-particle state can be occupied by at most M particles, with M≥ 1. For M = 1 and M = ∞, we recover the usual fermion and boson cases. We will focus on the case when the particles do not interact with each other, and the single particle quantum states i have energies ;. Assume that the system is in equilibrium at temperature T and chemical potential μ. (a) (b) (c) above. Calculate the appropriate partition function for the system in the conditions discussed Compute, as a function of temperature and chemical potential, the average occupation number (n) for state i, and find simplified expressions in the low and high temperature limits. For M1, does the system have the analog of a Fermi energy, i.e. an energy at which

Imagine a certain kind of particle, such that each single-particle state can be occupied by at most M particles, with M≥ 1. For M = 1 and M = ∞, we recover the usual fermion and boson cases. We will focus on the case when the particles do not interact with each other, and the single particle quantum states i have energies ;. Assume that the system is in equilibrium at temperature T and chemical potential μ. (a) (b) (c) above. Calculate the appropriate partition function for the system in the conditions discussed Compute, as a function of temperature and chemical potential, the average occupation number (n) for state i, and find simplified expressions in the low and high temperature limits. For M1, does the system have the analog of a Fermi energy, i.e. an energy at which

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1. Cannot be! Imagine a certain kind of particle, such that each single-particle state can be occupied by at most M particles, with M > 1. For M = 1 and M = ∞, we recover the usual fermion and boson cases. We will focus on the case when the particles do not interact with each other, and the single particle quantum states i have energies e¿. Assume that the system is in equilibrium at temperature T and chemical potential μ. (a) (b) (c) above. Calculate the appropriate partition function for the system in the conditions discussed Compute, as a function of temperature and chemical potential, the average occupation number (n) for state i, and find simplified expressions in the low and high temperature limits. For M1, does the system have the analog of a Fermi energy, i.e. an energy at which the occupation number is discontinuous at T = 0?
Transcribed Image Text:1. Cannot be! Imagine a certain kind of particle, such that each single-particle state can be occupied by at most M particles, with M > 1. For M = 1 and M = ∞, we recover the usual fermion and boson cases. We will focus on the case when the particles do not interact with each other, and the single particle quantum states i have energies e¿. Assume that the system is in equilibrium at temperature T and chemical potential μ. (a) (b) (c) above. Calculate the appropriate partition function for the system in the conditions discussed Compute, as a function of temperature and chemical potential, the average occupation number (n) for state i, and find simplified expressions in the low and high temperature limits. For M1, does the system have the analog of a Fermi energy, i.e. an energy at which the occupation number is discontinuous at T = 0?
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