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Consider a gas of indistinguishable non-interacting, non-relativistic, bosons of mass m and spin zero ind dimensions. a) Show that whether or not the gas will undergo Bose-Einstein condensation at sufficiently low temperature depends on the dimensionality d, and that in particular there is no Bose-Einstein condensation in d=2 dimensions. b) For the cases where there is Bose-Einstein condensation, find the condensation temperature T.. c) For the cases where there is Bose-Einstein condensation, how does the density of particles in the condenstate vary with temperature as T varies from T=0 to T=T?

Consider a gas of indistinguishable non-interacting, non-relativistic, bosons of mass m and spin zero ind dimensions. a) Show that whether or not the gas will undergo Bose-Einstein condensation at sufficiently low temperature depends on the dimensionality d, and that in particular there is no Bose-Einstein condensation in d=2 dimensions. b) For the cases where there is Bose-Einstein condensation, find the condensation temperature T.. c) For the cases where there is Bose-Einstein condensation, how does the density of particles in the condenstate vary with temperature as T varies from T=0 to T=T?

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Consider a gas of indistinguishable non-interacting, non-relativistic, bosons of mass m and spin zero ind dimensions. a) Show that whether or not the gas will undergo Bose-Einstein condensation at sufficiently low temperature depends on the dimensionality d, and that in particular there is no Bose-Einstein condensation in d=2 dimensions. b) For the cases where there is Bose-Einstein condensation, find the condensation temperature T.. c) For the cases where there is Bose-Einstein condensation, how does the density of particles in the condenstate vary with temperature as T varies from T=0 to T=T?
Transcribed Image Text:Consider a gas of indistinguishable non-interacting, non-relativistic, bosons of mass m and spin zero ind dimensions. a) Show that whether or not the gas will undergo Bose-Einstein condensation at sufficiently low temperature depends on the dimensionality d, and that in particular there is no Bose-Einstein condensation in d=2 dimensions. b) For the cases where there is Bose-Einstein condensation, find the condensation temperature T.. c) For the cases where there is Bose-Einstein condensation, how does the density of particles in the condenstate vary with temperature as T varies from T=0 to T=T?
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