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Paper Abstract and Keywords
Presentation 2014-11-17 11:40
Perturbative calculations of the energy spectrum for a quantum particle confined in weakly curved pipes
Shin-itiro Goto (IMS)
Abstract (in Japanese) (See Japanese page) 
(in English) A geometrical perturbation scheme that addresses some aspects of the Schr¨odinger equation for a single particle confined in a class of curved pipes is established. For our analysis the pipe will be regarded as a perturbed finitely long hollow cuboid. The perturbation will maintain the pipe’s rectangular cross-section while deforming its axis into a planar space-curve with, in general, non-constant curvature. It is assumed that the curvature $kappa (z)$ depends on the arc-length $|z|$ of the planar space-curve. Furthermore we require that $|kappa (z)L| ≪ 1$ with $L$ being
a length of the rectangular cross-section for the perturbation analysis to be effective. It is also assumed that the confinement is modeled with the 3-dimensional infinite potential well. Under these conditions the energy spectrum of the Schr¨odinger equation for a non-relativistic particle confined with the 3-dimensional infinite potential well, corresponding to a prescribed curved pipe, will be considered. A perturbation scheme will be applied to calculate a normalized wave function and a spectrum as a perturbation expansion in powers of $L$. Mode expansions based on
Dirichlet eigen-functions of the Laplacian for a rectangular domain can be used to reduce the general problem at each order. Since it will turn out that there exist some resonance terms in the course of our perturbative analysis,
a singlar perturbation method will be employed to deal with such resonance terms. This methodology gives a perturbative expression of the energy spectrum.
Keyword (in Japanese) (See Japanese page) 
(in English) Schrodinger equation / perturbation method / infinite potential well / Frenet-Serret formulae / / / /  
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Conference Information
Committee QIT  
Conference Date 2014-11-17 - 2014-11-18 
Place (in Japanese) (See Japanese page) 
Place (in English) Tohoku Univ. 
Topics (in Japanese) (See Japanese page) 
Topics (in English) Quantum Information 
Paper Information
Registration To QIT 
Conference Code 2014-11-QIT 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Perturbative calculations of the energy spectrum for a quantum particle confined in weakly curved pipes 
Sub Title (in English)  
Keyword(1) Schrodinger equation  
Keyword(2) perturbation method  
Keyword(3) infinite potential well  
Keyword(4) Frenet-Serret formulae  
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1st Author's Name Shin-itiro Goto  
1st Author's Affiliation Institute for Molecular Science (IMS)
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Speaker Author-1 
Date Time 2014-11-17 11:40:00 
Presentation Time 20 minutes 
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