I started my PhD in physics approximately a month ago. Now I am working on my first project with my advisor and a postdoc that follows me. I made several big mistakes for a little task that my advisor gave me, and now I feel really bad. They were stupid big mistakes that put me in a bad light, as if I didn't understand anything. It seems that I really didn't understand concepts.
I have the bad habit of always waiting for instructions, without taking initiative because in my past studies, professors usually told me what to do next as little exercises. I also have the bad habit of doing things mindlessly and not reviewing them, often resulting in errors.
I know that I am capable of completing this PhD and that I have the possibilities of doing very very well. I have the mental resources to do it(hardware) but the problem are my bad habits(software).
Now I am facing the problem that it will be harder for me to build trust with my advisor. What steps could I take to start building it again? Does a bad start affect things in the long run(like if my first two month are bad, but then I finish great my first year and do well on the other years, will my references for a possible postdoc be bad)?
I am slowly reading articles and concentrating on my little tasks, trying to understand everything I do. Apart from that I don't know what else to do.
Edit: Thank you very much! I will take all your advice and go ahead! Good luck also for the other PhDs