Abstract :
We propose a semiclassical method for calculating tunneling splittings, Δn1n2 of the vibrationally excited states in 2D ‘squeezed’ potential. Semiclassical wavefunctions in the classically forbidden region are found in the vicinity of the extreme real trajectory in the inverted potential, and 2D version of the Lifshitzʹ formula, which relates splitting to the probability flux through the dividing plane, is employed to calculate Δn1n2 Computations have been performed for different values of coupling strength and anharmonicity parameter. The results are compared with exact splittings and wavefunctions obtained by diagonalization of the 2D Hamiltonian. It is shown, that for small positive and arbitrary negative couplings the WKB method is accurate enough to reproduce correctly the change of tunneling splitting in progressions. WKB wavefunctions are in reasonable agreement with the exact ones in this case. Disagreement shows up with increasing C>0 for high vibrational levels, when extreme trajectories of other types can come into play.
