A Supersymmetric Approach to Excited States via Quantum Monte Carlo

Details A Supersymmetric Approach to Excited States via Quantum Monte Carlo A Supersymmetric Approach to Excited States via Quantum Monte Carlo

2009-03-27

arxiv.org/abs/0903.4827v3

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

We present here a supersymmetric (SUSY) approach for determining excitation energies within the context of a quantum Monte Carlo scheme. By using the fact that SUSY quantum mechanics gives rises to a series of isospectral Hamiltonians, we show that Monte Carlo ground-state calculations in the SUSY partners can be used to reconstruct accurately both the spectrum and states of an arbitrary Schr\"odinger equation. Since the ground-state of each partner potential is node-less, we avoid any ``node''-problem typically associated with the Monte Carlo technique. While we provide an example of using this approach to determine the tunneling states in a double-well potential, the method is applicable to any 1D potential problem. We conclude by discussing the extension to higher dimensions.

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