Why in the following paper Hamiltonian is minus center of mass kinetic energy operator?
doi:10.1088/0034-4885/70/12/R03
I've not read the entire paper but i think the answer is in the nature of the systems the author is investigating.The systems are clustered(bound) which implies they are at negative potential wrt an external observer.So if we reverse the signs of the terms we get a positive Tcm with a negative total Hamiltonian analogous with the semi-classical bohr treatment of the bound atom.
That would then imply that we are taking the centre of mass of the clustered system as the reference of the system thus the need to subtract individual kinetic energy terms T_i .That explains the negative T_i term present in the equation.
Dear Carringtone Kinyanjui;
Thanks for your answer! But why we should take the center of mass of the clusters as a reference for this system?
Best Regards;
Hadiseh Shirzadi
I think that might simplify computation,but it will not change the result of the Hamiltonian eigenvalues either way.Another clearer reason is that it easily shows the clustered nucleon system to be a bound state.
Why we don't see similar term in molecular Hamiltonian? There is no need to subtract the center of mass of atomic kinetic energy in molecular Hamiltonian.
Actually I think the term is existent in molecular hamiltonians please check http://en.wikipedia.org/wiki/Molecular_Hamiltonian for more details specifically the Schrodinger equation for the coulomb hamiltonian.The H' term has got an analogous term when you consider C.O.M motions.
In any bound complex system the kinetic energy of the center of mass must be substracted to get the binding energy and the internal excitation energies (the energy spectrum), otherwise different configurations may have different contributions from spurious COM motion (i. e., collective traslation). In some systems and for low excitation energies these contributions and their differences are very small and can be neglected.
Dear E. Moya de Guerra ;
Thanks for your answer! Is it true that a reason is we don't have anything in nuclear physics like Born-Oppenheimer approximation that subtracts this term automatic in molecular systems?
Best Regards;
Hadiseh
Dear E. Moya de Guerra ;
Thanks for your answer! Is it true that a reason is we don't have anything in nuclear physics like Born-Oppenheimer approximation that subtracts this term automatically in molecular systems?
Best Regards;
Hadiseh
- Badges
- Science topic
- Similar topics
- Phytochemistry
- Extracts