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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| Published in | Canadian journal of physics Vol. 89; no. 9; pp. 903 - 913 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Ottawa
NRC Research Press
01.09.2011
Canadian Science Publishing NRC Research Press |
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| Abstract | 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. |
|---|---|
| AbstractList | 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 sub(tip) = t sub(0)C sub(1)exp[C sub(2)(r/r sub(0)) super(9)], where t sub(0) is the time scale, C sub(1) and C sub(2) are constants of order unity, r is the radius of the cylinder, and r sub(0) is the length scale for the tipping. We compare our results with those found in previous works.Original Abstract: Nous obtenons les Hamiltoniens, classique et quantique, pour un cylindre soumis a des contraintes holonomes. Le Hamiltonien quantique est simplifie et recrit sous une forme sans dimension. Nous calculons le temps de bascule d'un cylindre quantique soumis a la gravite. Des solutions numeriques sont obtenues pour une fonction d'onde initiale appropriee. Cela nous donne un temps de bascule de la forme t sub(tip) = t sub(0)C sub(1)exp[C sub(2)(r/r sub(0)) super(9)], ou t sub(0) est l'echelle de temps de bascule, C sub(1) et C sub(2) sont des constantes de l'ordre de 1, r est le rayon du cylindre et r sub(0) est l'echelle de longueur pour le mouvement de bascule. Nous comparons nos resultats avec ceux de travaux precedents. 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. 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 [.sub.tip] = [t.sub.0][C.sub.1] exp [[C.sub.2][(r/[r.sub.0]).sup.9]], where [t.sub.0] is the time scale, [C.sub.1] and [C.sub.2] are constants of order unity, r is the radius of the cylinder, and r0 is the length scale for the tipping. We compare our results with those found in previous works. 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. 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 = t0C1 exp [C2(r/r0)9], where t0 is the time scale, C1 and C2 are constants of order unity, r is the radius of the cylinder, and r0 is the length scale for the tipping. We compare our results with those found in previous works. 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 ..., where ... is the time scale, C... and C... are constants of order unity, ... is the radius of the cylinder, and ... is the length scale for the tipping. We compare our results with those found in previous works. (ProQuest: ... denotes formulae/symbols omitted.) 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 [.sub.tip] = [t.sub.0][C.sub.1] exp [[C.sub.2][(r/[r.sub.0]).sup.9]], where [t.sub.0] is the time scale, [C.sub.1] and [C.sub.2] are constants of order unity, r is the radius of the cylinder, and r0 is the length scale for the tipping. We compare our results with those found in previous works. PACS Nos: 03.65.-w, 03.65.Xp Nous obtenons les Hamiltoniens, classique et quantique, pour un cylindre soumis a des contraintes holonomes. Le Hamiltonien quantique est simplifie et recrit sous une forme sans dimension. Nous calculons le temps de bascule d'un cylindre quantique soumis a la gravite. Des solutions numeriques sont obtenues pour une fonction d'onde initiale appropriee. Cela nous donne un temps de bascule de la forme [.sub.tip] = [t.sub.o][C.sub.1] exp [[C.sub.2][(r/[r.sub.0]).sup.9]], ou [t.sub.o] est l'echelle de temps de bascule, [C.sub.1] et [C.sub.2] sont des constantes de l'ordre de 1, r est le rayon du cylindre et [r.sub.0] est l'echelle de longueur pour le mouvement de bascule. Nous comparons nos resultats avec ceux de travaux precedents. [Traduit par la Redaction] |
| Abstract_FL | Nous obtenons les Hamiltoniens, classique et quantique, pour un cylindre soumis à des contraintes holonomes. Le Hamiltonien quantique est simplifié et récrit sous une forme sans dimension. Nous calculons le temps de bascule d’un cylindre quantique soumis à la gravité. Des solutions numériques sont obtenues pour une fonction d’onde initiale appropriée. Cela nous donne un temps de bascule de la forme 〈t〉
tip
= t
0
C
1
exp [C
2
(r/r
0
)
9
], où t
0
est l’échelle de temps de bascule, C
1
et C
2
sont des constantes de l’ordre de 1, r est le rayon du cylindre et r
0
est l’échelle de longueur pour le mouvement de bascule. Nous comparons nos résultats avec ceux de travaux précédents. |
| Audience | Academic |
| Author | Kellett, Ian Stoker, Jamie Sanchez-Fortun Shegelski, Mark R.A. |
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| Snippet | The classical and quantum mechanical Hamiltonians for a cylinder subject to holonomic constraints are derived. The quantum mechanical Hamiltonian is simplified... |
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| SubjectTerms | 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 |
| Title | Tipping time of a holonomic quantum cylinder |
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