New system-specific coherent states for bound state calculations

• Published in: Journal of physics. A, Mathematical and theoretical Vol. 45; no. 50; pp. 505302 - 14
• Main Authors: Chou, Chia-Chun, Biamonte, Mason T, Bodmann, Bernhard G, Kouri, Donald J
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 21.12.2012; IOP
• Subjects: Coherence; Dynamical systems; Dynamics; Exact sciences and technology; Ground state; Mathematical analysis; Mathematical models; Oscillators; Physics; Quantum theory; Operator; Quantum system; Uncertainty; Ground states; Bound state; Generating function; Excited states; Supersymmetric quantum mechanics; Harmonic oscillators; Double well model; Anharmonic oscillators; Superpotential; Wave functions; Morse potential; Coherent states
• ISSN: 1751-8113; 1751-8121
• DOI: 10.1088/1751-8113/45/50/505302

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.