Exploring sequential quantum adiabatic switching across supersymmetric partners for finding the eigenstates of a system

We demonstrate that one can exhaustively determine the n‐bound eigenstates of a Hamiltonian H by constructing a sequence of supersymmetric (SUSY) partner Hamiltonians and invoking a time‐dependent quantum adiabatic switching algorithm for passage from the ground state of one to the other. The ground states of the initial pair H⁽⁰⁾ and H⁽¹⁾ are constructed by solving the Riccati equation for the superpotential ?⁽⁰⁾ for H⁽⁰⁾ and adiabatically switching from the ground state Ψ of H⁽⁰⁾ to the ground state Ψ of H⁽¹⁾. The charge operator Q is then used to recover the first excited state Ψ of H⁽⁰⁾. The procedure is repeated for the ground states of SUSY pairs H^{(n + 1)} and H^{(n + 2)}, and appropriate charge operators lead to the excited states Ψ of H⁽⁰⁾ with , thereby exhausting the full eigenspectrum of H⁽⁰⁾. The workability of the proposed method is shown with several well‐known examples. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011