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##### Simulations / Euler angles in orientation.m

« Last post by**johncprice**on

*September 25, 2016, 01:24:12 AM*»

I have a question about Euler angles in Spinach.

I created a set of spin coordinates, rotated them using Euler angles (alpha,beta,gamma), and then created the full dipole Hamiltonian using

spin_system=assume(spin_system,'nmr');

[H,Q]=hamiltonian(spin_system,'comm');

H1=H+orientation(Q,[0,0,0]);

Now I do the same thing another way, by creating a spin system using the un-rotated coordinates and passing the Euler angles to orientation.m as follows:

spin_system=assume(spin_system,'nmr');

[H,Q]=hamiltonian(spin_system,'comm');

H2=H+orientation(Q,[gamma,-beta,alpha]);

It works! The two Hamiltonians are the same to high precision for various values of the angles.

But the call to orientation(Q,[gamma,-beta,alpha]) suggests to me that I am using the wrong Euler angle convention. I am using the one given in Kuprov's lecture sd_m2_lecture_03.pdf which corresponds to gamma rotation about z, beta rotation about y, alpha rotation about z. Is a different one being used?

I created a set of spin coordinates, rotated them using Euler angles (alpha,beta,gamma), and then created the full dipole Hamiltonian using

spin_system=assume(spin_system,'nmr');

[H,Q]=hamiltonian(spin_system,'comm');

H1=H+orientation(Q,[0,0,0]);

Now I do the same thing another way, by creating a spin system using the un-rotated coordinates and passing the Euler angles to orientation.m as follows:

spin_system=assume(spin_system,'nmr');

[H,Q]=hamiltonian(spin_system,'comm');

H2=H+orientation(Q,[gamma,-beta,alpha]);

It works! The two Hamiltonians are the same to high precision for various values of the angles.

But the call to orientation(Q,[gamma,-beta,alpha]) suggests to me that I am using the wrong Euler angle convention. I am using the one given in Kuprov's lecture sd_m2_lecture_03.pdf which corresponds to gamma rotation about z, beta rotation about y, alpha rotation about z. Is a different one being used?