System-specific coherent states are constructed based on the formulation of supersymmetric quantum mechanics for arbitrary quantum systems. By regarding the superpotential as a generalized displacement variable, we identity the ground state of a quantum system as the minimizer of the supersymmetric Heisenberg uncertainty product. A special case is the ground state of the standard harmonic oscillator. One constructs standard coherent states by applying a shift operator to a ‘fiducial function’, taken as the ground state Gaussian. By analogy, we use the ground state for any other system as a new fiducial function, generating from its shifts new dynamically-adapted, overcomplete coherent states. The discretized system-specific coherent states can serve as a dynamically-adapted basis for bound state calculations. Accurate computational results for the Morse potential, the double well potential and the two-dimensional anharmonic oscillator systems demonstrate that the system-specific coherent states can provide rapidly-converging approximations for excited state energies and wave functions.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.