New system-specific coherent states for bound state calculations

作者：Chou Chia Chun^*; Biamonte Mason T; Bodmann Bernhard G; Kouri Donald J

来源：Journal of Physics A-Mathematical and Theoretical, 2012, 45(50): 505302.

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 %26apos;fiducial function%26apos;, 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.

• 出版日期2012-12-21