# Use of Rotate left to shift a band structure

I have to apply a shift to a periodic band structure. A simple example would be

A=Table[{j,Cos[j]},{j, -3 \[Pi]/4, 3 \[Pi]/4, \[Pi]/2}]
B=Table[{j,Cos[j+\[Pi]/2]},{j, -3 \[Pi]/4, 3 \[Pi]/4, \[Pi]/2}]


In my case the band structure is much more complicated and is obtained numerically. Since the bands are periodic in k space I'd like to avoid computing them again for the shifted k-vector, but instead obtain the shifted bands 'rotating' the list in which I have the eigenvalues and the k-grid. I was suggested that this should be possible using RotateLeft/Right, but I am not sure how exactly. If someone has had a similar problem or has an idea I'd use some help

• You mean A = Table[{j, Cos[j], j}, {j, -3 \[Pi]/4, 3 \[Pi]/4, \[Pi]/2}] B = Table[{j, Cos[j + \[Pi]/2], j}, {j, -3 \[Pi]/4, 3 \[Pi]/4, \[Pi]/2}] ? – wuyudi May 25 at 14:50
• Sorry there was a Typo in the example now it should be correct. – Leone di Mauro May 25 at 14:58

It is straightforward to rotate a list either to the left or to the right.

The syntax is simply RotateLeft[list,k] in order to rotate the elements of the List list, k positions to the left.

For example, check the output of

RotateLeft[A, 2]


and likewise the output

RotateRight[A, 2]


and compare them to the original list given by A.

Using this minimal example, you should be able to get a firm grasp on how the RotateLeft/Right works. Hopefully, you can apply this to the example of interest.