Tipping time of a holonomic quantum cylinder

The classical and quantum mechanical Hamiltonians for a cylinder subject to holonomic constraints are derived. The quantum mechanical Hamiltonian is simplified and cast into a dimensionless form. The tipping time of a quantum mechanical cylinder subject to gravity is calculated. Numerical solutions...

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Bibliographic Details
Published inCanadian journal of physics Vol. 89; no. 9; pp. 903 - 913
Main Authors Shegelski, Mark R.A., Stoker, Jamie Sanchez-Fortun, Kellett, Ian
Format Journal Article
LanguageEnglish
Published Ottawa NRC Research Press 01.09.2011
Canadian Science Publishing NRC Research Press
Subjects
03.65.Xp
03.65.–w
Constants
Cylinders
Dimensional analysis
Gravitation
Gravity
Hamiltonian functions
Mathematical analysis
Mathematical models
Numerical analysis
Quantum mechanics
Quantum physics
Rayon
Unity
Wave functions
Canada
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Summary:The classical and quantum mechanical Hamiltonians for a cylinder subject to holonomic constraints are derived. The quantum mechanical Hamiltonian is simplified and cast into a dimensionless form. The tipping time of a quantum mechanical cylinder subject to gravity is calculated. Numerical solutions for an appropriate initial wave function are obtained. We find that the tipping time is given by 〈t〉 tip = t 0 C 1  exp [C 2 (r/r 0 ) 9 ], where t 0 is the time scale, C 1 and C 2 are constants of order unity, r is the radius of the cylinder, and r 0 is the length scale for the tipping. We compare our results with those found in previous works.
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ISSN:0008-4204
1208-6045
DOI:10.1139/p11-086