Classical, Quantum and Event-by-Event Simulation of a Stern–Gerlach Experiment with Neutrons
Abstract
1. Introduction
2. Neutron Experiment
3. Newtonian Mechanics
3.1. Model for the Magnetic Field
3.2. Analytically Solvable Cases
3.3. Model Parameters
3.4. Numerical Solution of Equation (3)
3.5. Newtonian Dynamics: Simulation Results for Neutrons
4. Quantum-Theoretical Model
4.1. Quantum Theory: Simulation Results
4.2. Quantum Theory: Simplified Model
5. Event-by-Event Simulation
- 4.
- If set ,
- 4.
- If : the first time that the event occurs, that is when the particle enters the region where , use Equation (16) with to align the vector along the magnetic field and compute .
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Large Static Field B0
Appendix B. Numerical Solution of Equation (3)
- ,
- ,
- ,
- ,
Appendix C. Newtonian Dynamics: Imaginary Silver Particles
Appendix D. Quantum-Theoretical Model
Appendix D.1. Momentum Representation
Appendix D.2. Textbook Model
Appendix D.3. Dimensionless Form
Appendix D.4. Initial State
Appendix D.5. Simulation Method
Appendix D.6. TDPE Solver: Technical Aspects
Appendix D.7. Quantum Dynamics: Imaginary Silver Particles
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Experiment | ??? | two spots (Figure 2) |
Newton | circular (Figure 3f) | one stripe (Figure 3a) |
Quantum theory | circular (Figure 8f) | two spots (Figure 8a) |
Event-by-event | circular (Figure 11f) | two spots (Figure 11a) |
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De Raedt, H.; Jin, F.; Michielsen, K. Classical, Quantum and Event-by-Event Simulation of a Stern–Gerlach Experiment with Neutrons. Entropy 2022, 24, 1143. https://doi.org/10.3390/e24081143
De Raedt H, Jin F, Michielsen K. Classical, Quantum and Event-by-Event Simulation of a Stern–Gerlach Experiment with Neutrons. Entropy. 2022; 24(8):1143. https://doi.org/10.3390/e24081143
Chicago/Turabian StyleDe Raedt, Hans, Fengping Jin, and Kristel Michielsen. 2022. "Classical, Quantum and Event-by-Event Simulation of a Stern–Gerlach Experiment with Neutrons" Entropy 24, no. 8: 1143. https://doi.org/10.3390/e24081143
APA StyleDe Raedt, H., Jin, F., & Michielsen, K. (2022). Classical, Quantum and Event-by-Event Simulation of a Stern–Gerlach Experiment with Neutrons. Entropy, 24(8), 1143. https://doi.org/10.3390/e24081143