Recent content by t00dles23

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    10 Electrons in an Infinitely Deep 1D Square Well

    Homework Statement An infinitely deep one-dimensional potential well has a width of 1 nm and contains 10 electrons. The system of electrons has the minimum total energy possible. What is the least energy, in eV, a photon must have in order to excite a ground-state electron in this system to the...
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    Topology - Use Componentwise Convergence Criterion to prove closed ball closed.

    Nevermind. I understand now. Thank you for your hint.
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    Topology - Use Componentwise Convergence Criterion to prove closed ball closed.

    I don't think I understand your hint. I mean sure, ||u_k|| --> ||c||. But I don't know what that does for me. It seems to just point back to the proof using ||c|| and the triangle inequality, but that doesn't use the componentwise convergence criterion. Can you elaborate?
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    Topology - Use Componentwise Convergence Criterion to prove closed ball closed.

    Homework Statement Let r be a positive number and define F = {u in R^n | ||u|| <= r}. Use the Componentwise Convergence Criterion to prove F is closed.Homework Equations The Componentwise Convergence Criterion states: If {uk} in F converges to c, then pi(uk) converges to pi(c). That is, the...
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    |a_1 + a_2 + + a_n| <= sqrt(n)*sqrt((a_1)^2 + (a_2)^2 + + (a_n)^2)

    Thank you for your reply. I got it figured out. It's essentially the RMS-AM inequality, which I realized by looking at the AM-GM inequality again and remembering that it is one part of a bigger statement. And happily, the RMS-AM part follows directly from the Cauchy-Schwarz inequality: Cauchy...
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    |a_1 + a_2 + + a_n| <= sqrt(n)*sqrt((a_1)^2 + (a_2)^2 + + (a_n)^2)

    Homework Statement For a natural number n and real numbers a1, a2,...,an, verify that: |a1 + a2 + ... + an| <= sqrt(n)*sqrt(a12 + a22 + ... + an2) Homework Equations I suspect that this can be done using properties of the inner product (i.e. the Cauchy-Schwarz inequality), or the triangle...
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    Is Berkley as competitive to get into as Yale or UCLA

    Berkeley is more competitive than UCLA, but not as much as Harvard or other Ivies. However, for people in California, it becomes much easier to get into UC schools. It is not difficult to get into a UC as a transfer from a community college in California - there are programs that each UC has to...
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    Schools UCSB College of Creative Studies

    I was considering going there for my undergrad. I liked it because it gave the small school environment even though UCSB is a big state school. I ended up going to a fairly well-known liberal arts school instead as I got much more money from them. However, I think that you'd learn much more at...
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    Special Relativity - geometric approach?

    http://physics.oregonstate.edu/~tevian/geometry/ Tevian Dray (who wrote this manuscript) gave a talk at my school once - the talk was very informative, and this is his manuscript for a textbook on it.
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    Schools Studying Physics at Reed College? Others?

    I'm currently a physics major at Reed. It's true that Griffiths just retired, but he'll still be teaching a class a year as an emeritus. Don't worry though, the entire faculty is great. Reed annually graduates about 18 physics majors per year, from a student body of about 1400. We also are in...
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    Books of mathematics for physics recommendation

    Mathematical Methods in the Physics Sciences by Mary Boas seems to be what you're looking for.
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    Programs Recommend Maths and CS Courses for Physics Major

    Complex Analysis is important. The application of CA class would probably be sufficient - as its main applications lie in physics. If you have room / time you could take regular CA I and II. Many people find complex analysis one of the more interesting math classes they take. As for...
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    Schools Navigating Grad School After Non-Ivy Undergrad Experience

    Basically none of the top schools in graduate physics offer terminal masters degree programs. You'd have to set your sights lower if you plan on just getting a masters. Or perhaps in your year off you can do research and figure out what field you'd like to pursue. Otherwise, you can just...