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07:46
Setting Limits on Supersymmetry Using Simplified Models
Published on: November 15, 2013
Supersymmetric approach to excited states
Eric R Bittner1, Jeremy B Maddox, Donald J Kouri
1Department of Chemistry, University of Houston, Houston, Texas 77204, USA. bittner@uh.edu
The Journal of Physical Chemistry. A
|November 19, 2009
Summary
This study introduces a novel supersymmetric (SUSY) quantum mechanics approach to accurately calculate quantum system excitation energies using quantum Monte Carlo methods, overcoming common limitations.
Area of Science:
- Quantum mechanics
- Computational physics
- Supersymmetry
Background:
- Quantum Monte Carlo (QMC) methods are powerful for ground-state calculations.
- A significant challenge in QMC is the 'node problem' for excited states.
- Supersymmetric (SUSY) quantum mechanics offers unique properties for solving quantum problems.
Purpose of the Study:
- To develop a new method for determining excitation energies using QMC.
- To leverage SUSY quantum mechanics to overcome the 'node problem' in QMC.
- To reconstruct the full spectrum and states of Schrödinger equations.
Main Methods:
- Utilized the isospectral property of SUSY quantum mechanics.
- Performed QMC ground-state calculations on SUSY partner potentials.
- Reconstructed the spectrum and states of the original Schrödinger equation.
Main Results:
- Successfully determined excitation energies and states without encountering the 'node' issue.
- Demonstrated the method's accuracy with an example of tunneling states in a double-well potential.
- Showcased the applicability to any one-dimensional potential.
Conclusions:
- The presented SUSY-QMC approach accurately calculates excitation energies and quantum states.
- The method circumvents the 'node' problem inherent in traditional QMC techniques.
- Future work includes extending the methodology to higher dimensions.
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