Symmetric Triple Well with Non-Equivalent Vacua: Simple Quantum Mechanical Approach

The structure of the energy levels in a deep triple well is analyzed using simple quantum mechanical considerations. The resultant spectra of the first three energy levels are found to be composed of a ground state localized at the central well and the two other states are distributed only among the left and right well in anti-symmetric and symmetric way respectively. Due to the tunneling effects the energy eigenvalue of the ground state is approximately equal to the ground state energy for a harmonic oscillator localized at the central well, while the two others are nearly degenerate with approximate values equal to the ground state energy of a harmonic oscillator localized at the left or right well. The resulting pattern of the spectra are confirmed numerically. The failure of the instantonic approach recently applied for predicting the correct spectra is commented