As you have noted each state in USA has different requirements. The general requirement are as follows:

 - Obtain a Bachelors in Engineering (BSE) from an ABET accredited engineering program. The disciplines that I am familiar are Electrical, Civil, and Mechanical. I suggest you review the references below of more detailed infomation. 
 - Successfully complete the Fundamentals in Engineering exam to obtain Engineering in Training (EIT) status
 - Gain professional experience (typically four years minimum)
 - Successfully complete the Professional Engineer exam.

Considering that you a have bachelors and graduate degree in physics you have few options:

 - Enroll in a ABET accredited engineering program to obtain Bachelors in Engineering. With your physics background you are most likely to get a significant amount of credit. It is likely that you will be able to obtain a Bachelors in Engineering in about 2 year depending on the University.
 - Submit your credential to the licensing authority hopeful they will accept your credentials and allow you sit for the EIT exam. You will have to do more research on this topic. I suggest that you review [**Washington Accord**][1].
 - If you are already a licensed practicing engineer submit those credentials to licensing authority. They may accept these credentials. I have submitted my USA credentials [Engineers Australia][2] and obtained registration in Australia of a Australian based engineering project. 


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**References:** 

 - [Washington Accord][3]
 - [What is the sequence of exams to become a Professional Engineer in California?][4]
 - [How To Get Licensed? (National society of Professional Engineers)][5]


  [1]: http://www.ieagreements.org/Washington-Accord/Washington-Accord-Overview.pdf
  [2]: https://www.engineersaustralia.org.au/national-engineering-register
  [3]: https://en.wikipedia.org/wiki/Washington_Accord
  [4]: http://engineering.stackexchange.com/a/5985/110
  [5]: http://www.nspe.org/resources/licensure/how-get-licensed