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In general, how hard is it to get a job in theoretical physics at a major research institution or university? What sort of credentials are required? I would assume a doctorate from someplace like Caltech or Princeton... am I right?

Depends on what you mean by a job. There are quite a lot of temporary jobs out there, for which all you need is a PhD (by the way, Caltech and Princeton are great undergrad institutions, but there are better places for graduate study in physics). In order to get a permanent job at a research institution or university you need:
1. PhD
2. Probably 4-6 years postdoctoral research experience
3. Probably 10-20 published papers (at least)
4. Evidence that you are able to obtain grant funding
5. Support of some prominent well-known person in your field.
6. Luck
The job situation is actually rather bleak - very few places are hiring physicists right now, and a lot are cutting back (through early retirement at universities, and outright firings or job transfers to non-research positions at other places). Note that teaching expertise is not a requirement...

Also note that your PhD does not have to be from a famous school, although it certainly helps. More important than where you went to school is what you are able to accomplish. Theoretical physics is particularly tough subfield of physics and here are a lot of good theorists out there who cannot get research-level faculty appointments; at least that is what they seem to be saying in Physics Today (the newsmagazine of the American Physical Society).


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