This paper, a continuation of [1], explores the energy spectrum of two stable particles in a finite volume, specifically focusing on how the energy eigenvalues vary with the box size \( L \). The author, M. Lüscher, demonstrates that the low-lying energy values can be expanded in an asymptotic power series of \( 1/L \). The coefficients in these expansions are related to the elastic scattering amplitude in a simple and universal manner. This relationship allows for the determination of the scattering amplitude at low energies if accurate calculations of two-particle energy values are possible, such as through numerical simulations. The motivation for this study is twofold: first, it aids in spectral analysis and interpretation of correlation functions in lattice theory simulations; second, it provides a method to calculate low-energy scattering amplitudes, which are otherwise difficult to compute directly in finite volume. In finite volume, the particle momenta are quantized, and the energy spectrum of two-particle states with zero total momentum is discrete. As \( L \) approaches infinity, the level spacing decreases, but it remains significant in practice, especially for large volumes. For a massive quantum field theory describing particles (mesons) with spin 0 and mass \( m \), the energy values of two-particle states are given by the free field expression plus a small correction due to meson interactions. The energy shift is influenced by polarization effects and direct interactions between the mesons. For large \( L \), the energy shift due to polarization effects decreases exponentially, while the direct interaction correction decays only as a power of \( 1/L \). This fundamental difference can be understood heuristically by noting that interactions in massive quantum field theories are short-ranged.This paper, a continuation of [1], explores the energy spectrum of two stable particles in a finite volume, specifically focusing on how the energy eigenvalues vary with the box size \( L \). The author, M. Lüscher, demonstrates that the low-lying energy values can be expanded in an asymptotic power series of \( 1/L \). The coefficients in these expansions are related to the elastic scattering amplitude in a simple and universal manner. This relationship allows for the determination of the scattering amplitude at low energies if accurate calculations of two-particle energy values are possible, such as through numerical simulations. The motivation for this study is twofold: first, it aids in spectral analysis and interpretation of correlation functions in lattice theory simulations; second, it provides a method to calculate low-energy scattering amplitudes, which are otherwise difficult to compute directly in finite volume. In finite volume, the particle momenta are quantized, and the energy spectrum of two-particle states with zero total momentum is discrete. As \( L \) approaches infinity, the level spacing decreases, but it remains significant in practice, especially for large volumes. For a massive quantum field theory describing particles (mesons) with spin 0 and mass \( m \), the energy values of two-particle states are given by the free field expression plus a small correction due to meson interactions. The energy shift is influenced by polarization effects and direct interactions between the mesons. For large \( L \), the energy shift due to polarization effects decreases exponentially, while the direct interaction correction decays only as a power of \( 1/L \). This fundamental difference can be understood heuristically by noting that interactions in massive quantum field theories are short-ranged.