Center of mass problem

[stefano]

I don't know how to treat a center of mass corrections.
Suppose to have a Slater determinant of N single-particle wavefunctions. If I make a traslation to center of mass of system, this is mean to move all particle in the following way:

R_i ---> R_i - (sum_j {R_j}/N)

But how have I to correct the gradient and laplacian terms?

I think that there would be a kinetic energy correction. Is it true?

Thank's!

[santoshroy]

Since the gradient and laplacian contain "coordinate" (d/dx, d2/dx2..)terms one has to replace to coordinate with c.m. coordinates, there will ofcourse will be a kinetic energy correction as K.E. contains terms like (d2/dx2).
In another words Physically kinetic energy is not invariant in different coordinate farmes.