- #1
sam_bell
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Hi. I'm reading an introductory section on the Bose-Einstein condensation of a non-interacting, spinless boson gas. I'm confused by the claim that the ground state is in a coherent state with eigenvalue sqrt(N0) exp(i theta), where N0 is the expected number of particles in the ground state. The justification is that the commutator [a0/sqrt(V), a0*/sqrt(V)] = 1/V goes to zero in the thermodynamic limit V = volume goes to infinity (a0 annihilation operator for ground state). Therefore a0 acts like a complex number and so the ground state must be in a coherent state. Huh? Who asked you to divide by V anyway? Totally opaque. And doesn't statistical mechanics say the system is in an ensemble of definite particle eigenstates with probability exp(-beta*mu*N)/Z (i.e. NOT a coherent superposition of definite particle states)?? Does someone understand this better?