The importance of motivational characteristics in physics education has been increasingly recognized in recent years, with prior studies establishing a framework for how students' identity as a physics person is composed of their perceived recognition by physics instructors and peers, along with their physics self-efficacy and interest. We seek to extend this research beyond introductory physics students by using five years of cross-sectional data collected from motivational surveys administered to physics majors throughout their undergraduate education and to the first-year physics Ph.D. students at a large research university in the US. We find that physics majors in the first year tend to respond to the motivational survey prompts more positively than their non-physics major peers, though with a smaller mean difference in self-efficacy than in the other motivational beliefs. Further, on average, the responses of physics majors over time from their first year of the undergraduate curriculum through the first year of graduate school remain largely consistent, indicating that students are constantly adjusting their interpretation of the survey items to match the current level of expertise in physics courses they are taking. Finally, consistent with prior studies with introductory physics students, we find that perceived recognition is the best predictor of physics identity for physics majors throughout their entire education in physics, pointing to the importance of physics instructors making a concerted effort to constantly recognize their students throughout as people who can excel in physics.