What do potential postdoc advisers seek in research statement letters? I am putting together my application for a postdoctoral position in theoretical condensed matter physics. The position is not a fellowship and is a regular postdoc position. If you have gone through the process of applying for such positions a number of times, or, even better, if you have reviewed such research statement letters, what are the main points that are sought/you seek in such letters? Specifically, should I put more emphasize on my PhD research to demonstrate my "depth of knowledge" on projects I have worked on (past research), or dwell more on things that I want/am capable to do (future research)?
Some of this depends a lot on field and laboratory, and I don't know the customs of physics.  As somebody who has dealt with this question in both biology and computer science, however, let me give you some thoughts:

Since you aren't aiming for a fellowship, you're probably going to be supported by a funded project of some sort.  That means the PI you'd be working for promised their funders they would get somebody do a postdoc-sized piece of work on Topic X.  Their biggest concern is thus likely to be whether you are the person who can do that. Accordingly, when I'm thinking about postdocs, the properties I'm looking for are:


Flexibility enough to shift from their Ph.D. topic to the topic of the project, which is pretty much guaranteed to be different.
Autonomy, creativity, and maturity enough to tackle their part of the project without much hand-holding.
Productivity and responsibility enough to deliver research progress at regular intervals.


Formulate your letter accordingly, showing what you have accomplished, that you are capable of formulating a research vision, and that you have interests outside of your research vision.  The goal is not to sell yourself, but to be interesting enough that it's worth the PIs time to talk to you in person, which is where the real decision will be made.

In fact, however, you are best served if you can skip the letter entirely and approach potential PIs in person at conferences or other meetings.  Get introductions from your advisor if you can.  Practice your elevator pitch (explaining what you'd put in a letter in just three spoken sentences).  Speaking as a PI, a whole lot of postdoc jobs ultimately originated by PIs talking at a meeting and one of them saying, "I've got this great student who's graduating, and I'll bet they'd fit well in your lab..." or the other saying, "I've got this grant starting next year and there's a gap I need to fill..."