Transition Amplitudes within the Stochastic Quantization Scheme
H. H\"uffel (Inst. f\"ur Theor. Phys., Univ. Wien), H. Nakazato, (Dept. of Phys., Univ. of the Ryukyus)
TL;DR
This paper demonstrates how to compute quantum transition amplitudes using stochastic quantization for various nonrelativistic systems, including particles in magnetic fields and Grassmann variables.
Contribution
It introduces a method for calculating transition amplitudes within stochastic quantization for multiple nonrelativistic quantum systems.
Findings
Successfully computed amplitudes for free particles, harmonic oscillators, and particles in magnetic fields.
Extended stochastic quantization to Grassmann quantum mechanics.
Provides a unified approach for different nonrelativistic quantum systems.
Abstract
Quantum mechanical transition amplitudes are calculated within the stochastic quantization scheme for the free nonrelativistic particle, the harmonic oscillator and the nonrelativistic particle in a constant magnetic field; we close with free Grassmann quantum mechanics.
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