The equivalence between the canonical and microcanonical ensembles when applied to large systems

A straightforward technique is suggested that demonstrates that a microcanonical ensemble and canonical ensemble behave in exactly the same way in the thermodynamic limit. The canonical distribution is derived for a closed system, without the need to introduce a large reservoir that exchanges energy with the system. The derivation also clarifies the issue of the energy interval which arises when introducing the microcanonical ensemble. (C) 2007 American Association of Physics Teachers.