Corrigendum to “Exact canonic eigenstates of the truncated Bogoliubov Hamiltonian in an interacting bosons gas” (Physica B: Condensed Matter (2016) 496 (38–44) (S0921452616302046)(10.1016/j.physb.2016.05.018))

In the author's paper ‘Exact canonic eigenstates of the truncated Bogoliubov Hamiltonian in an interacting bosons gas’ (Physica B, 2016, pg. 38–44), an error occurred in identifying the eigenvalue ES(k) (Eq. no. (25c)) of the Hamiltonian h˜c(k) (Eq. no. (17b)) with the eigenvalue ES(k) of Hamiltonian Hc (Eq. no. (5)). The correct claim is, instead, ES(k)=2ES(k), since in the sum Eq. no. (17a) the eigenvalue of h˜c(k)=h˜c(−k) is to be counted twice. Due to this error, the symbol ES(k) in the 15-th line (from bottom) of pg 40 must be replaced by ES(k), and the last sentence in pg. 40: /In Section 4 it will be shown that… of the s-eigenstates/must be modified as follows: In Section 4 it will be shown that ESBCA(k)=ES(k)/2, i.e. that the BCA energy eigenvalues are half those of the s-eigenstates. In pg. 41, just after Eq. no. (25c) and the sentence/with k and N restored/, one should insert: Notice that: (25d) ES(k)=2ES(k),i.e. the eigenvalues ES(k) of Hc are twice as large as those of h˜c, since they must be counted twice in the sum Eq. no. (17a). In pg. 42, just after 4. Comparison and discussion, the sentence: /the exact eigenvalues… (Eq. (6))/ must be replaced by: the exact eigenvalues ES(k), corresponding to the s-eigenstates |S,k〉c, are twice as large as the energies ESBCA(k) obtained in Section 2 (Eq. (6)). At the end of pg 42 (7-th line from bottom), the whole initial sentence/In short:… are exact/ must be dropped. Eq. no. (35) must be corrected by replacing ϵ(k) with 2ϵ(k) in the exponential. The corrections indicated do not change the meaning and the spirit of the paper. Rather, they support even more the main result that the exact eigenstates of Hc and those obtained under BCA are quite different, since at this stage it is clear that the eigenvalues too are different (ES(k)=2ESBCA(k)). This is expected to lead to non trivial physical consequences, as will be shown in a forthcoming paper.