Stochastic simulation of quantum mechanics
Simon M. Catterall, Ian T. Drummond, R. R. Horgan · Journal of Physics A Mathematical and General · 1991
Langevin methods have proved useful in simulating lattice field theories of many kinds. These methods are essentially a practical realization of the stochastic quantization approach to quantum mechanical systems. The authors wish to show that the Langevin method is effective in calculations of non-relativistic quantum mechanical systems. For a one-dimensional system a more conventional approach through the diagonalization of the Hamiltonian matrix using the method of Sturm sequencing is more efficient. However, in two and higher dimensions where the Hamiltonian is no longer tridiagonal the Langevin scheme is more efficient and accurate. It follows therefore that Langevin methods may actually have a great deal to offer in quantum mechanical problems in high dimensions especially in cases where the potential does not have spherical symmetry.