<p>I don’t think you have a great chance chance at Caltech, Stanford etc. just because your GPA and scores are on the low side. If these schools are your dream schools there is no harm in applying except for ~$150 application fees.</p>
<p>You self studying sounds really cool and if you want to study quantum physics, I would suggest looking at some LAC’s that have have excellent physics programs and would be more interested in your self studying rather than your stats. </p>
<p>Hope this helps! Good Luck!</p>