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n维耦合谐振子的能量谱条件数理论研究
Theoretical Study of Energy Spectrum Condition Number of n-Dimension Coupled Harmonic Oscillator
DOI: 10.12677/MP.2012.24013, PDF, HTML, 下载: 3,429  浏览: 11,216  科研立项经费支持

Abstract: This paper according to the matrix form of Schrödinger equation of n-dimension coupled harmonic oscillator, on the basis of representation theory, the element of matrix Hnn of Hamiltonian operator ˆH is derived. Through con-structing one of complete normed linear space, the Hnn is proved to be boundedness in this space by using functional theory, and eigenvalue E of Hamiltonian operator is obtained; and then the author get the spectrum condition number formula of E that is made use of matrix theory. From this expressions, the formula of operator norm of energy E and harmonic oscillator’s state is acquired. Researching the relationship between spectrum condition number of E and operator norm, the supremum and infimum of E operator norm is estimated, the reason of numerical size of energy spectrum condition number is presented. It turned out that: when the approximately range of spectrum condition number and operator norm is achieved, under the representation theory frame, the difference degree between two states of har-monic oscillator are estimated, which in terms of the exactly value of spectrum condition number, and analysis the fea-ture states of harmonic oscillator.

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