# Quantum Trajectories: Real or Surreal?

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## Abstract

**:**

## 1. Introduction

## 2. Re-Examination of the Analysis of ESSW

#### 2.1. General Results Using Wave Packets

#### 2.2. What Can Be Said about the Behaviour of Individual Particles?

## 3. The Bohm Approach When Spin Is Included

#### 3.1. Spin and the Use of the Pauli Equation

## 4. Detailed Calculation of the Trajectories

#### 4.1. One Stern-Gerlach Magnet

#### 4.2. Numerical Values for Single Stern-Gerlach Magnet

#### 4.3. Two Stern-Gerlach Magnets

#### 4.4. The Appearance of the Quantum Torque

#### 4.5. Detailed Calculation of the Quantum Potential

#### 4.6. Numerical Details: Quantum Potential Single Stern-Gerlach Magnet

#### 4.7. Numerical Details: Quantum Potential in Two SG Magnet Case

## 5. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

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**Figure 7.**Trajectories with spin vectors overlaid on the spin quantum potential immediately on exiting a single SG magnet.

**Figure 8.**${Q}_{trans}$ (

**left**) and ${Q}_{spin}$ (

**right**) quantum potential for a two SG magnets system.

**Figure 9.**Trajectories with spin vectors overlaid on the spin quantum potential for a two SG magnet system.

Atom | Ag |
---|---|

Mass | $1.8\times {10}^{-25}$ Kg |

Width of magnets | 4 and $8\times {10}^{-4}$ m |

Length of magnets | 1 and $2\times {10}^{-2}$ m |

Velocity of atoms | ${v}_{y}=y/t=500$ m/s |

Time within magnets | $\Delta t=2$ and $4\times {10}^{-5}$ s |

Magnetic field strength at centre | ${B}_{0}=5$ Tesla |

Magnetic field gradient | ${B}_{0}^{\prime}=1000$ Tesla/m |

Wave packet width | $\sigma =1\times {10}^{-4}$ m |

Wave packet speed | $u={\mu}_{B}{B}_{0}^{\prime}\Delta t/m=1$ m/s |

${\Delta}^{\prime}={\mu}_{B}{B}_{0}^{\prime}\Delta t\hslash =mu/\hslash $ | ${\Delta}^{\prime}=1.717\times {10}^{9}$ m${}^{-1}$ |

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**MDPI and ACS Style**

Hiley, B.J.; Van Reeth, P.
Quantum Trajectories: Real or Surreal? *Entropy* **2018**, *20*, 353.
https://doi.org/10.3390/e20050353

**AMA Style**

Hiley BJ, Van Reeth P.
Quantum Trajectories: Real or Surreal? *Entropy*. 2018; 20(5):353.
https://doi.org/10.3390/e20050353

**Chicago/Turabian Style**

Hiley, Basil J., and Peter Van Reeth.
2018. "Quantum Trajectories: Real or Surreal?" *Entropy* 20, no. 5: 353.
https://doi.org/10.3390/e20050353