### Abstract

We apply our invertibility of quantum mechanical systems concept to design open loop controls of molecular systems. The inverse quantum-mechanical control of molecules is studied using the equation of motion for the expectation value of an operator. With this method a requisite external field is obtained to exactly track a prescribed molecular objective expectation value as a function of time. Applications to diatomic molecules are formulated. While the method is directly applicable as a test of physical intuition, it can in principle be used to design fields for specific objectives including reactive selectivity. Results are presented for energy tracking in the hydrogen fluoride molecular system. The numerical calculations show that seemingly benign objective tracks may give rise to singularities in the field. However, these singularities do not present problems in the evolution of the dynamical quantities and instead provide useful hints for designing robust fields.

Original language | English |
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Title of host publication | Proceedings of the IEEE Conference on Decision and Control |

Publisher | Publ by IEEE |

Pages | 1930-1935 |

Number of pages | 6 |

Volume | 2 |

ISBN (Print) | 0780312988 |

Publication status | Published - 1 Dec 1993 |

Externally published | Yes |

Event | Proceedings of the 32nd IEEE Conference on Decision and Control. Part 2 (of 4) - San Antonio, TX, USA Duration: 15 Dec 1993 → 17 Dec 1993 |

### Other

Other | Proceedings of the 32nd IEEE Conference on Decision and Control. Part 2 (of 4) |
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City | San Antonio, TX, USA |

Period | 15/12/93 → 17/12/93 |

### Fingerprint

### ASJC Scopus subject areas

- Control and Systems Engineering
- Modelling and Simulation
- Control and Optimization

### Cite this

*Proceedings of the IEEE Conference on Decision and Control*(Vol. 2, pp. 1930-1935). Publ by IEEE.

**Inverse control of quantum-mechanical systems : Some application studies.** / Huang, Garng Morton; Gross, Peter; Singh, Harjinder; Rabitz, Herschel; Mease, Kenneth.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the IEEE Conference on Decision and Control.*vol. 2, Publ by IEEE, pp. 1930-1935, Proceedings of the 32nd IEEE Conference on Decision and Control. Part 2 (of 4), San Antonio, TX, USA, 15/12/93.

}

TY - GEN

T1 - Inverse control of quantum-mechanical systems

T2 - Some application studies

AU - Huang, Garng Morton

AU - Gross, Peter

AU - Singh, Harjinder

AU - Rabitz, Herschel

AU - Mease, Kenneth

PY - 1993/12/1

Y1 - 1993/12/1

N2 - We apply our invertibility of quantum mechanical systems concept to design open loop controls of molecular systems. The inverse quantum-mechanical control of molecules is studied using the equation of motion for the expectation value of an operator. With this method a requisite external field is obtained to exactly track a prescribed molecular objective expectation value as a function of time. Applications to diatomic molecules are formulated. While the method is directly applicable as a test of physical intuition, it can in principle be used to design fields for specific objectives including reactive selectivity. Results are presented for energy tracking in the hydrogen fluoride molecular system. The numerical calculations show that seemingly benign objective tracks may give rise to singularities in the field. However, these singularities do not present problems in the evolution of the dynamical quantities and instead provide useful hints for designing robust fields.

AB - We apply our invertibility of quantum mechanical systems concept to design open loop controls of molecular systems. The inverse quantum-mechanical control of molecules is studied using the equation of motion for the expectation value of an operator. With this method a requisite external field is obtained to exactly track a prescribed molecular objective expectation value as a function of time. Applications to diatomic molecules are formulated. While the method is directly applicable as a test of physical intuition, it can in principle be used to design fields for specific objectives including reactive selectivity. Results are presented for energy tracking in the hydrogen fluoride molecular system. The numerical calculations show that seemingly benign objective tracks may give rise to singularities in the field. However, these singularities do not present problems in the evolution of the dynamical quantities and instead provide useful hints for designing robust fields.

UR - http://www.scopus.com/inward/record.url?scp=0027875133&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027875133&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0027875133

SN - 0780312988

VL - 2

SP - 1930

EP - 1935

BT - Proceedings of the IEEE Conference on Decision and Control

PB - Publ by IEEE

ER -