Can a ground state energy be negative?

[Kites]

Just a short question.

I have five energies.

-25 eV
-5 eV
0 eV
5 eV
25 eV

The textbook definition is that the ground state is the state with the lowest energy, i.e. I believe 0 in this case.

But that is taking the absolute value of theenergies.

In reality the lowest energy is -25 eV so is it instead actually the -25 eV in this case

 

[Ygggdrasil]

Yes, energies can be negative, so -25eV is the correct answer. The way that energy is defined, it's not really the numerical value of the energy that is important (it's completely arbitrary), but it's the energy differences that matter. So, you could define the five energies as 0, 20, 25, 30, and 50eV and the system would pretty much be the same (although you could not compare these energies measured from a system using a different reference point).