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arXiv · 0903.4827

A Supersymmetric Approach to Excited States via Quantum Monte Carlo

Eric R. Bittner·Jeremy B. Maddox·Donald J. Kouri
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Abstract

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 Schrödinger 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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Eric R. Bittner, Jeremy B. Maddox, Donald J. Kouri. 2009-06-18. A Supersymmetric Approach to Excited States via Quantum Monte Carlo. https://arxiv.org/abs/0903.4827

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