Abstract
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?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 x, y and z 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.
Highlights
Quantum mechanical rotation operators in explicit forms are the essential tools of microscopic systems
Rotation operators of other spins greater than 1/2 can be found numerically by evaluating the series expansions of exponential operator obtained from Schrödinger equation, by evaluation of Wigner-d formula or by recently established expressions in polynomial forms discussed in the text
It seems necessary to establish the theoretical foundations of large spin systems
Summary
Quantum mechanical rotation operators in explicit forms are the essential tools of microscopic systems. Pulsed nuclear magnetic resonance, (pulsed-NMRnuclear magnetic resonance), pulsed electron paramagnetic resonance (pulsed-EPRElectron paramagnetic resonance) and pulsed electron nuclear double resonance (pulsedENDORElectron nuclear double resonance) spectroscopies, utilizes rotation operators in rotating coordinate system or laboratory coordinate system where the spins are polarized along a definite orientation by a known external magnetic field. This direction is defined as z axis and a series of magnetic pulses are applied along laboratory x and/or y axes to rotate the polarized spins around related axes [11] [12] [13] [14] [15]. In this work explicit rotation operator expressions of angular momenta 5/2 to 7/2 are constructed from exponential operators given in equality below for x, y and z components of angular momenta for a series of angles θ between interval θ1 to θN , and fitting the obtained values to suitable functions by linear curve fitting procedure
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