I'm surprised no one has caught this yet. You would see yellow, not green. 580 nm is smack dab in the middle of the spectral yellows (570 nm to 590 nm). Green (spectral green) is light between 520 and 570 nm.
@bobie, notice that I said spectral yellow and spectral green. Imagine a screen that is white except for a colored circle in the middle. Imagine that that colored circle emits light of one frequency only, and that that single frequency can be made to slowly vary from the deepest red to the deepest violet. You will see the colors of the rainbow as the frequency gradually changes from red to orange to yellow to green to blue and finally to violet. Those are the spectral colors.
Most people have three kinds of cones in their eyes. The behavior of those cones is dictated by chemistry and physics. Some cones respond strongest to reddish light, others to greenish light, and yet others to blue/violet. The response curves of these three kinds of cones overlap. Both the red and green cones will respond fairly strongly to that 580 nm laser light; the blue cones will not respond much at all. We see the different colors of the rainbow because different frequencies elicit different combinations of responses from those three kinds of cones.
Is that all there is to color? Absolutely not. There are very, very few pure light sources in nature. Almost all of the colored objects we see have a broad spectrum of light coming from them into our eyes. Going back to that colored circle on white background, let's change that central circle so that emits multiple frequencies of light at once. Two key results show up.
1. Metamers.
Tune the frequencies produced just right and you'll get a response from the cones that is indistinguishable from a pure spectral color. The manufacturers of computer screens take full advantage of this effect. Your computer screen does not produce yellow light. So how does it produce this?
If you aren't colorblind you should see that central block as yellow, even though there is no yellow light coming from your screen. The light coming into your eyes is a combination of red and green light that elicits the same response as would spectral yellow. So you see yellow.
2. Non-spectral colors.
We see more colors than just the colors of the rainbow. That white background, for example. There is no such thing as spectral white. White is a non-spectral color. Another even more interesting one is purple. Our eyes do something rather funky with the spectrum. The full spectrum of electromagnetic radiation goes from radio to gamma. Visible light is but a tiny, tiny part of that full spectrum. In terms of the spectrum, there is no such thing as the color wheel. That violet turns into purple, then magenta, and then red: That's something our vision system does that is distinct from frequency.
That's just biophysics. There's a lot more to color perception than this low level, biophysical description of how you see color.