I don't think you have to provide a lot of personal details in your SOP. For example, I think what you've told us on this thread here is more than enough. Actually, I don't even think you need to mention depression and PTSD specifically.
If you have any resources now, e.g. a health professional, or someone in the health office at your old school / current work that you can talk to, maybe they can also give good advice on how to demonstrate that you are now capable of completing graduate studies now.
Personally, I think all you really have to say in your SOP is that you were not able to complete your original PhD programs due to health reasons. You can then say that you have resolved these issues and you are now ready to handle graduate studies again. I think the best way to convince the committee of this is to speak about what you've accomplished since leaving your first graduate program. For example, starting work again is a good sign.
The SOP -- Statement of Purpose -- does not have to be personal. I view it as a professional account of your background and what you hope to achieve in graduate school. Some schools ask for a "Personal Statement" or a "Personal History Statement" and this is where you can tell your more personal stories if you wish. However, I don't think telling your stories in full detail is going to be more convincing than simply stating that there was a problem and you've now overcome it. If they don't believe you, then telling the details isn't going to make a difference -- it's still just you saying "I'm ready now". The best way is to show that things have changed instead of just saying it has.
In addition, I also feel that the admissions committees are NOT health professionals, so they should not expect to hear about applicants' full history and they should not be the ones judging whether or not the applicant is "healthy enough" to attend graduate school. Instead, their job is to look at your qualifications and experience and judge whether or not you are qualified enough to succeed in their program. The only reason to mention your health problem is to explain that your previous program dismissal was not due to the lack of your physics ability and qualifications.
I know there are some profs that serve on admissions committees on this forum -- maybe they can give more relevant feedback. But my opinion is that you should not have to disclose anything personal and the admissions committees should not expect you to either.