To pursue research career in physics; How much physics courses should I pass in my undergraduate engineering degree?
Cross-disciplinary movement does happen fairly frequently, particularly between engineering and the mathematical and physical sciences. Unfortunately, as the academic disciplines themselves become more cross-disciplinary, it becomes much harder to say what specific training one needs to move from one field to another between the undergraduate and graduate levels. 

A good way to check for the qualifications you are likely to need is to examine the course requirements of schools you're already interested in attending as a graduate student—if your undergraduate program has sufficient depth in math and physics to allow you to take those courses as a graduate student, then an admissions committee will likely be OK with the lateral movement. 

If you have questions about what is necessary, you can contact the person in charge of admissions at some of the departments you're interested in for further clarification.