I'm an undergraduate who is going to apply for scholarships and to graduate school in physics in the coming months. At the start of last semester in August, I tried to join a group of a respected professor, where I was assigned a theoretical project. I've met with him maybe three times during the few coming weeks, before we mutually agreed that the assigned problem is pretty much a dead end. The professor had no idea for another suitable project, so I decided to join a different group, with which I stayed until very recently, when an analogous issue occured (but in this case I have actually done some work until that happened).
I was debating whether this "project" deserves being mentioned in my resume, at least for the sake of continuity, and so far have received contrary pieces of advice. Currently, that project is listed on my resume as follows:
Worked with […] at […] on a project attempting to reformulate the definition of quantum-mechanical work for autonomous Hamiltonians.
I am certainly not going to ask for a letter of recommendation from that professor since there are others who know me much better. I only want to know whether the inclusion of the above description in my resume would have a positive or negative influence on my application.