Physics – Condensed Matter – Other Condensed Matter
Scientific paper
2012-01-09
Physics
Condensed Matter
Other Condensed Matter
15 pages, 2 figures, submitted in PRB, v3: corrections in text
Scientific paper
We determine the structure of exact wave functions of the ground (\Psi_0) and excited (\Psi_k) states of He II under zero boundary conditions (BCs). The solutions take the form \Psi_0=(formula) and \Psi_k =(formula 2). The explicit account for boundaries leads to a significant change of the equations for \Psi_0 and \Psi_k and the theoretical values of the energy of quasiparticles E(k) and the energy of the ground state E_0, as compared with the solutions for periodic BCs. In the limit of a weak interaction, we obtain the formula E(k) = \sqrt{(h^{2} k^2/2m)^{2} + [n\nu_{3}(k)/8][h^2 k^2/m]}, which differs from the well-known Bogolyubov formula by the factor 1/8. The effect of boundaries is related to the different collections of eigenmodes for closed and open system. We advance also the idea of the relation of the \lambda-transition to the multiple creation of rotons with zero energy.
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