The discussion revolves around the integration involving Euler angle rotation matrices, particularly in the context of quantum mechanics and coordinate transformations. Participants explore the properties of these matrices, their determinants, and implications for rotations acting on spin states.
Participants express differing views on the properties of the matrices, particularly regarding their determinants and invertibility. There is no consensus on the correct approach to the integral or the implications of the matrices in the context of quantum mechanics.
Limitations include the potential misunderstanding of quantum mechanics principles by some participants and the unresolved nature of the integral involving Euler angles. The discussion reflects a mix of expertise levels, which may affect the clarity of the mathematical arguments presented.
Individuals interested in the mathematical aspects of quantum mechanics, particularly those dealing with rotation matrices and integrals, as well as those working on coordinate transformations in robotics.
Hello, thanks for your reply. I made a mistake of Sz matrix, and I just updated the correct matrix. Those two matrices do have a determine as well as trace equal to 0 because those matrices are the matrix representation of Sz and S^2 operator of spin 1/2 1/2 system in Quantum Mechanics. The three exponential inside the integral represents the rotation.Svein said:
Yes, because those rotations are acting on spins. For example, if We act this rotation operator related to Sz on an eigenstate |00>, we will get e^(0) = 1 as our result, and we can not reverse our process. Since our eigenvalue of |00> corresponding to the Sz operator is just 0.Svein said:
