### Abstract

The rotation operator approach proposed previously is applied to spin dynamics in a time-varying magnetic field. The evolution of the wave function is described, and that of the density operator is also treated in terms of a spherical tensor operator base. It is shown that this formulation provides a straightforward calculation of accumulated phases and probabilities of spin transitions and coherence evolutions. The technique focuses, not on the rotation matrix, but on the three Euler angles and its characteristic equations are equivalent to the Euler geometric equations long known to describe the motion of a rigid body. The method usually depends on numerical calculations, but analytical solutions exist in some situations. In this paper, as examples, a hyperbolic secant pulse is solved analytically, and a Gaussian-shaped pulse is calculated numerically.

Original language | English (US) |
---|---|

Pages (from-to) | 6424-6429 |

Number of pages | 6 |

Journal | The Journal of Chemical Physics |

Volume | 101 |

Issue number | 8 |

State | Published - 1994 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*The Journal of Chemical Physics*,

*101*(8), 6424-6429.

**Rotation operator approach to spin dynamics and the Euler geometric equations.** / Zhou, Jinyuan; Ye, Chaohui; Sanctuary, B. C.

Research output: Contribution to journal › Article

*The Journal of Chemical Physics*, vol. 101, no. 8, pp. 6424-6429.

}

TY - JOUR

T1 - Rotation operator approach to spin dynamics and the Euler geometric equations

AU - Zhou, Jinyuan

AU - Ye, Chaohui

AU - Sanctuary, B. C.

PY - 1994

Y1 - 1994

N2 - The rotation operator approach proposed previously is applied to spin dynamics in a time-varying magnetic field. The evolution of the wave function is described, and that of the density operator is also treated in terms of a spherical tensor operator base. It is shown that this formulation provides a straightforward calculation of accumulated phases and probabilities of spin transitions and coherence evolutions. The technique focuses, not on the rotation matrix, but on the three Euler angles and its characteristic equations are equivalent to the Euler geometric equations long known to describe the motion of a rigid body. The method usually depends on numerical calculations, but analytical solutions exist in some situations. In this paper, as examples, a hyperbolic secant pulse is solved analytically, and a Gaussian-shaped pulse is calculated numerically.

AB - The rotation operator approach proposed previously is applied to spin dynamics in a time-varying magnetic field. The evolution of the wave function is described, and that of the density operator is also treated in terms of a spherical tensor operator base. It is shown that this formulation provides a straightforward calculation of accumulated phases and probabilities of spin transitions and coherence evolutions. The technique focuses, not on the rotation matrix, but on the three Euler angles and its characteristic equations are equivalent to the Euler geometric equations long known to describe the motion of a rigid body. The method usually depends on numerical calculations, but analytical solutions exist in some situations. In this paper, as examples, a hyperbolic secant pulse is solved analytically, and a Gaussian-shaped pulse is calculated numerically.

UR - http://www.scopus.com/inward/record.url?scp=0001346250&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001346250&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0001346250

VL - 101

SP - 6424

EP - 6429

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 8

ER -