Abstract
An investigation is made of the implications that the presence of a Bose condensate (BC) has for the form of the many particle Schroedinger wavefunction. It is shown that many particle wavefunctions of states which contribute to the BC, contain long range structure in the position space of each particle. It follows from the requirement that the wavefunction is single valued that, in the presence of a BC, the angular momentum of each particle must be quantised over macroscopic length scales. The paper thus provides a new and simple proof from first principles, that Bose condensation implies macroscopic quantum behaviour. It is shown that this behaviour can be described in terms of the occupation by each particle of the same single particle-like macroscopic wavefunction. The structure in position space of this wavefunction is investigated, using a well known model of the many particle wavefunction for the ground state of 4He. The model predicts that the probability density of each particle is delocalised in the presence of a BC, occupying all spaces in the sample volume, from which the particle is not excluded by the hard core interaction with other particles.
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Mayers, J. A New Approach to Bose Condensation and Superfluidity in 4He. J Low Temp Phys 109, 135–152 (1997). https://doi.org/10.1007/s10909-005-0080-6
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DOI: https://doi.org/10.1007/s10909-005-0080-6