I'm sorry, but I feel what you are saying, and what everyone else has said, goes entirely against the spirit of the question. Everyone is posting this information on how amps affect the sound of a pair of headphones, and I have found this information over and over, posted by many different people, but the question I am asking is about where the scientific evidence for this information is? I want peer reviewed articles, academic publishings. Yet, I can't find them anywhere. Yes, everyone is telling me that amps do have an affect, and they explain in what way, but testimonials aren't what I am looking for.
you really need to name the headphone model and the soundcard to get any useful advice - and soundcards and amps seldom have comprehensive specs in their manuals - even for the limited purpose of checking if I, V capabilities are adequate
This also goes against the spirit of the question, as this will not provide any sort of scientific evidence and understanding, it will just provide more testimonial evidence on a specific product. I'm not looking for any specific product, the assumption is that I don't own any (because I don't, the only amp I have is a FiiO E11,and the highest impedance headphone I have is the HD 280s).
To be brutally honest and probably make a ton of people really mad? I don't believe amps do anything that a human ear could discern. Machines and computers can, of course, but not humans. I believe I could plug some HD 800s into my motherboard and have no difference between that and a $2000 amp. But you know what? I have no proof of that. I have zero evidence that what I say is true.
In fact, it is very likely I am wrong. And thats why I'm here. Me saying that amps are useless is just as useless to everyone as saying amps are the most important piece of audio equipment to have, unless the person saying it has empirical evidence to back it up. But so far, it looks like that evidence doesn't exist. So, the other question is, why? How does an industry where equipment that goes for thousands of dollars not have any scientific studies that they are actually useful? That makes no sense to me. Or maybe I'm just bad a Google...
edit: bolded for emphasis