One-dimensional multiple-well oscillators: A time-dependent quantum mechanical approach

Time-dependent Schrödinger equation (TDSE) is solved numerically to calculate the ground- and first three excited-state energies, expectation values 〈x2j〉, j=1, 2 …, 6, and probability densities of quantum mechanical multiple-well oscillators. An imaginary-time evolution technique, coupled with the minimization of energy expectation value to reach a global minimum, subject to orthogonality constraint (for excited states) has been employed. Pseudodegeneracy in symmetric, deep multiple-well potentials, probability densities and the effect of an asymmetry parameter on pseudodegeneracy are discussed.