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## Homework Statement

If I have a Hamiltonian matrix, [itex]\mathcal{H}[/itex], that only depends on a kinetic energy operator, do the energy eigenvalues have to be non-negative? I have an [itex]\mathcal{H}[/itex] like this, and some of its eigenvalues are negative, so I was wondering if they have any physical significance, or if I should just reject them and their associates eigenstates. Also, one of the eigenstates was just the zero vector, which I think can be ignored since it's a trivial solution.

## Homework Equations

[itex]\mathcal{H} = \mathcal{K} + \mathcal{V} = \mathcal{K}[/itex]

## The Attempt at a Solution

I don't see any way that the system could have negative energy if the potential is zero everywhere, but I also don't feel entirely comfortable just ignoring eigenstates like that.