(Received August 6, 1957)
Recently, Matsubara and Matsuda1) proposed a lattice model of liquid helium. In their papers, the derivation of the Hamiltonian function for the lattice gas (substance) is not quite clear and subject to some questions. The most important of the question will be “whether the anti-commutativity of annihilation and creation operators of a lattice site does not destroy the Bose property of the system under consideration?”. In this note, the Hamiltonian of the lattice gas, which reduces to that of liquid helium when the lattice constant is taken to be infinitesimal, is derived by the use of the formalism of second quantization. And it is confirmed that the calculations by Matsubara and Matsuda are surely for the Bose lattice gas (substance) when two particles cannot occupy a lattice site at the same time.
URL :
http://ptp.ipap.jp/link?PTP/18/462/
DOI : 10.1143/PTP.18.462