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The Quantum Mechanical Rotation Operators of Spins 5/2 to 7/2

The Quantum Mechanical Rotation Operators of Spins 5/2 to 7/2
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摘要 With the creation of logic gates and algorithms for quantum computers and entering our lives, it is predicted that great developments will take place in this area and important efforts are made. Spin rotation processors are quantum mechanical rotation processors and have no classic counterparts. The rotation operators of spin 1/2 are well known and can be found in related textbooks. But rotation operators of other spins greater than 1/2 can be found numerically by evaluating the series expansions of exponential operator obtained from Schr<span style="white-space:nowrap;">?</span>dinger equation, by evaluation of Wigner-d formula or by recently established expressions in polynomial forms discussed in the text. In a previous paper, rotation operators for spins 1/2 to 2 were published. In this work, explicit symbolic expressions of <em>x</em>, <em></em><em>y</em> and <em>z</em> components of rotation operators for spin 5/2, 3 and 7/2 are worked via exponential operator for each element of related spin operators and utilizing simple linear curve fitting process. The procedures gave out exact expressions of each element of the rotation operators. With the creation of logic gates and algorithms for quantum computers and entering our lives, it is predicted that great developments will take place in this area and important efforts are made. Spin rotation processors are quantum mechanical rotation processors and have no classic counterparts. The rotation operators of spin 1/2 are well known and can be found in related textbooks. But rotation operators of other spins greater than 1/2 can be found numerically by evaluating the series expansions of exponential operator obtained from Schr<span style="white-space:nowrap;">?</span>dinger equation, by evaluation of Wigner-d formula or by recently established expressions in polynomial forms discussed in the text. In a previous paper, rotation operators for spins 1/2 to 2 were published. In this work, explicit symbolic expressions of <em>x</em>, <em></em><em>y</em> and <em>z</em> components of rotation operators for spin 5/2, 3 and 7/2 are worked via exponential operator for each element of related spin operators and utilizing simple linear curve fitting process. The procedures gave out exact expressions of each element of the rotation operators.
作者 Mehpeyker Kocako&#231 Recep Tapramaz Mehpeyker Kocako&#231;;Recep Tapramaz(Department of Computer Technologies, Vocational School of &#304;mamo&#287;lu, &#199;ukurova University, Adana, Turkey;Department of Physics, Ondokuz May&#305;s University, Samsun, Turkey)
出处 《Journal of Applied Mathematics and Physics》 2021年第5期856-863,共8页 应用数学与应用物理(英文)
关键词 Rotation Operator Quantum Information Systems SPIN Electron Paramagnetic Resonance (EPR) Rotation Operator Quantum Information Systems Spin Electron Paramagnetic Resonance (EPR)
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