Tamil Selvam Murugaya, Nurisya Mohd Shah, Sharifah Kartini Said Husain
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引用次数: 0
Abstract
We wrote this paper to study in detail the mathematical methods used in deriving the parameters 𝑝𝑝′1, 𝑝𝑝′2, 𝑥𝑥′1, 𝑥𝑥′2, 𝑀𝑀, 𝐾𝐾 and 𝑒𝑒2𝜂𝜂 in the research papers by Han et al. (1999), Makarov (2018a), Han et al. (1993), and Han et al. (1995) to find the Schmidt modes 𝛬𝛬𝑘𝑘 in quantum entanglement. Here, we have analysed and developed a thorough calculation in exploring the rationales behind the existence of these parameters in two and three-coupled harmonic oscillators. Various mathematical approaches were applied in the study, ranging from polynomials and linear algebra to trigonometry and the Pythagorean theorem. We found the parameters 𝐾𝐾 and 𝑒𝑒2𝜂𝜂 using the matrices’ determinants and eigenvalues. With these rationales in deriving the parameters 𝐾𝐾 and 𝑒𝑒2𝜂𝜂 in the research papers for the two-coupled harmonic oscillators, we have formulated similar parameters for three-coupled harmonic oscillators as the conclusion of our study.
期刊介绍:
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