About undergraduate admission in Cambridge

Short answer: yes

Long answer: The *college* admissions tutor might not be, and (s)he will read your PS. But your PS will also be read by the physics academics who review your application. Since it is these academics who ultimately decide who gets the offers, it is safe to assume the reader has a good knowledge of the subject area.

EDIT: Despite having written that, it has occurred to me that my own PS (I applied for maths, and got an offer) was in fact readable by somebody who hadn't done any advanced maths. My PS mostly talked about mathsy things I had done. For example, the kind of thing I put on there was, 'I did the senior maths challenge and got X award.' I also mentioned something like, 'I worked out how to prove that, if, in a game of Tennis, each player has a 50% chance of winning each point, then the player who serves has a 60% chance (or whatever) of winning the set'. Whilst this is 'actual maths', it is still accessible to the layman.

There is another form which you fill in, called the SAQ. It's an online form which Cambridge send you. On that I put something like, 'I have been thinking about the relation between the Physics equations F=GMm/r^2 and potential=GMm/r', and got asked briefly about that in interview.

BTW Your personal statement should be about you. Therefore do not waste time explaining that 'Quantum mechanics is very different from classical mechanics. For example, Schrodinger's cat says...'. Instead, phrase it as, (e.g.) 'I have been reading about Heisenberg's uncertainty principle. The probabilistic nature of QM intrigues me, as it is quite different from the classical stuff I am doing at school. I read that the uncertainty of a wavefunction is minimised when it takes the form of a Gaussian wavepacket, and am trying to relate this to the material on normal distributions and the central limit theorem which have been covered in my probability classes.' [But only say that if it's true, in case you get asked about it! If this example looks scarily sophisticated, don't be worried; in my own PS I didn't go into any degree-level stuff in detail.]

Offtopic I know, but have you got some interesting sources about qm and the CLT stuff? I'm really interested