A NEW APPROACH TO BOSE-CONDENSATION AND SUPERFLUIDITY IN HE-4

An investigation is made of the implications that the presence of a Bo se condensate (BC) has for the form of the many particle Schroedinger wavefunction. It is shown that many particle wavefunctions of states w hich contribute to the BC, contain long range structure in the positio n space of each particle. It follows from the requirement that the wav efunction is single valued that, in the presence of a BC, the angular momentum of each particle must be quantised over macroscopic length sc ales. The paper thus provides a new and simple proof from first princi ples, that Bose condensation implies macroscopic quantum behaviour. It is shown that this behaviour can be described in terms of the occupat ion by each particle of the same single particle-like macroscopic wave function. The structure in position space of this wavefunction is inve stigated, using a well known model of the many particle wavefunction f or the ground state of He-4. The model predicts that the probability d ensity of each particle is delocalised in the presence of a BC, occupy ing all spaces in the sample volume, from which the particle is not ex cluded by the hard core interaction with other particles.