Quantum mechanical rotation operators are the subject of quantum mechanics, mathematics and pulsed magnetic resonance spectroscopies, namely NMR, EPR and ENDOR. They are also necessary for spin based quantum information systems. 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 Schrödinger equation, or by evaluating Wigner-d formula or by evaluating recently established expressions in polynomial forms discussed in the text. In this work, explicit symbolic expressions of x, y and z components of rotation operators for spins 1 to 2 are worked out by evaluating series expansion of exponential operator for each element of operators and utilizing linear curve fitting process. The procedures gave out exact expressions of each element of the rotation operators. The operators of spins greater than 2 are under study and will be published in a separate paper.
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25 March 2016
9TH INTERNATIONAL PHYSICS CONFERENCE OF THE BALKAN PHYSICAL UNION (BPU-9)
24–27 August 2015
Istanbul, Turkey
Research Article|
March 25 2016
Explicit expressions of quantum mechanical rotation operators for spins 1 to 2
Mehpeyker Kocakoç;
Recep Tapramaz
a)
Corresponding author: mkocakoc@cu.edu.tr
AIP Conf. Proc. 1722, 200009 (2016)
Citation
Mehpeyker Kocakoç, Recep Tapramaz; Explicit expressions of quantum mechanical rotation operators for spins 1 to 2. AIP Conf. Proc. 25 March 2016; 1722 (1): 200009. https://doi.org/10.1063/1.4944224
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