What is the energy of a particle

[jaydnul]

When we do a standard QM calculation we get energy eigenvalues. So, for example in the ground state of a hydrogen atom, does that energy value include the mass-energy of the particle. Does it include the thermal energy? Or is it just the kinetic plus potential energy?

 

[The_Duck]

It includes whatever is included in the Hamiltonian. For the most basic hydrogen atom this is just kinetic energy and electric potential energy.

Note that thermal energy is not a property of individual particles. Thermal energy in thermodynamics or statistical mechanics is part of an approximate description of systems of many particles.

 

[jaydnul]

I see. Thanks

 

[mfb]

You could add the mass-energy manually (just by adding mc^2 to the Hamiltonian).

If you calculate the energy with relativistic quantum mechanics, you automatically include the mass-energy in the Hamiltonian.