### Abstract

The solutions of the axisymmetric circular cylinder quantum nano jet can be governed by the time-dependent linear Schrödinger equation that is solved by two approaches. One is a partial analytic method based on the Fourier-Bessel transform and the other is numerical method based on finite difference methods. Appropriate boundary conditions for the solutions of the circular cylinder quantum nano jet are derived. By the Fourier-Bessel transform method, several integral formulas for the solutions of the jet are obtained. The Gaussian quadrature numerical integration is then applied to evaluate the integrals. The fourth-order central and compact difference methods are used for the numerical approach. The fourth-order Runge-Kutta time integration is applied for the time marching. Detailed comparisons between the partial analytic and numerical methods are performed. The results indicate that the partial analytic method can obtain right solutions and the proposed numerical method can capture the dispersion wave very well.

Original language | English |
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Title of host publication | 4th AIAA Theoretical Fluid Mechanics Meeting |

Publication status | Published - 2005 |

Event | 4th AIAA Theoretical Fluid Mechanics Meeting - Toronto, ON, Canada Duration: 2005 Jun 6 → 2005 Jun 9 |

### Other

Other | 4th AIAA Theoretical Fluid Mechanics Meeting |
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Country | Canada |

City | Toronto, ON |

Period | 05-06-06 → 05-06-09 |

### All Science Journal Classification (ASJC) codes

- Mechanical Engineering
- Mechanics of Materials
- Condensed Matter Physics

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## Cite this

*4th AIAA Theoretical Fluid Mechanics Meeting*