Generalization of Feynman's Theory of Energy Levels of Liquid Helium

Feynman’s method of finding the lower energy levels of liquid helium is generalized to include energy levels corresponding to a number of excitons. The expectation values of momentum in these levels are calculated. Our extension is valid so long as the number of excitons is small compared with that of atoms, and no pair of excitons with wave numbers equal in magnitude but opposite in sign co-exists. The excitons derived according to our scheme are found to behave as bosons. The interaction potential between helium and the surrounding wall can be regarded as a creation and an annihilation operator of the excitons. The usual hypothesis for the critical velocity is discussed in this connection.