I have been trying to work with a certain professor for a year, since the time I joined PhD. I wasn't paid by her, rather, funded by TAships.
This past quarter, I did a project for a class I took with her. Her student, who was the TA for the course, was super super super helpful, and was basically the driving force for the project.
The thing is, I really like this topic and want to continue working on it. Unfortunately, this professor has still not warmed up to me. She still gives me a very unclear response of whether or not she wants to take me as a student and has told me she'll tell me in a couple of weeks. Since summer is approaching, I really want to finalize an advisor ASAP, or at least someone who would supervise at least one research project for me. I am sick of not having a supervisor for research, as despite having topics that interest me, I am unable to find specific problems to work on.
Anyway, my question is - I have given up on this professor saying yes to me at all, so I am writing to other professors; would it be ethical for me to continue my current project with whoever agrees to supervise me? I am, of course, assuming here that someone will agree to do that, but just in case that happens, is it okay for me to do this?
The project was for a class project, was not funded by this professor Iam trying to impress,but it was a very theoretical one, and the idea, the methods, everything was her student's (who was the TA for the class).