Energy Level for a Type of Three-Particle Hamiltonian with Kinetic Couplings

For a triatomic molecule described by the Harniltonian with kinetic energy couplings, H = P²₁/(2m) +P²₂/(2m) + P²₃/(2M) + kP₁P₂ + KP₁P₃ + KP₂P₃ + V₁(X₂–X₁ ) + V₂x₃ - ( X₁+ X₂) / 2 , its energy level formula is derived. The cases are consider when the potentials V_i (i = 1,2) are harmonic oscillator, or Morse potential, separately. Squeezing mechanism involved in the approach for solving this dynamic problem is revealed.