Recent content by phys2

I think that that modern day democracies are pretty stable. I mean, you do get protests and economic crisis, but certainly not what you would associate with the breakup of the USSR or the demise of empires. Politicwatcher.

Well, every civilisation is different, culturally, from each other so it is hard to find a general system of how a civilisation develops. I did a course on Ancient Greece at university and my final essay was on how the Greek system of government, the polis, developed. To sum up 5000 words in a...

Ahh I see thanks Yes, it works out...thanks

Homework Statement The problem is : Let S = [ (1,-1,3) , (-1,3, -7) , (2,1,0) ]. Do the vectors u = (5,1,3) and v = (2,3,6) belong to span(S) Homework Equations The Attempt at a Solution So span means that I could take linear combinations of u and v and they should end up...

Yes, I finally get it now. Using the same method, I should be able to get through all the problems. Thanks a lot for your help!

Oh, I think I get it. What we have done so far is find vectors that belong or do not belong to S. Example: v = (1,2) does not belong to S and v= (1,1) belongs to S. But v = (1,1), even if it belongs to S, that does not necessarily make it a vector space, I need to do do the addition and scalar...

(2,2) is not in S because 22 = 4 and 23 = 8 and 4≠8. I am still confused about showing that S is not closed under addition and scalar multiplication. With addition, I know that the axiom is u + v = v + u So if I take v = (2,2), u = (1,2), do I just do it the normal vector addition...

Yea, that is really the part (b) of the problem that I faced. I don't think I can take v = (1,1) though since both numbers have to be different x12 - x23 Anyway, even if I take two different numbers, what I get is another number. How do I know whether that number is part of set S or not? For...

Homework Statement Hi, I am really having trouble with questions regarding proving whether a given set is a vector space or not. So one of the questions is [ x ε R2|x12=x23 ] So I have to prove whether the following set is a vector space Homework Equations The Attempt at a...

Homework Statement A physical system is designed having the following equation of motion md2x/dt2 + c(dx/dt) - kx = 0. (a) From the corresponding subsidiary equation, find the solution to this equation of motion. (HINT: use the solution of the damped harmonic oscillator as a guide)...

So I got -h(bar)2/2m (4β2x2) ψ + 1/2mω2x2ψ = Hamiltonian Hψ=Eψ?

Homework Statement A particle moves in a one dimensional potential : V(x) = 1/2(mω2x Show that the function ψ(x) = a0exp(-βx2) is an eigenfunction for the Hamiltonian for a suitable value of β and calculate the value of energy E1 Homework Equations The Attempt at a Solution...

Homework Statement Ok I have attached the pdf file and I have a problem with velocity phase spaces (Question 3a). Honestly, the lecture notes were not very helpful and looking online and in textbooks, they talked about solving Lagrange's equations but nothing to deal with the problem of Q3...

Does anyone have an answer? :biggrin:

Homework Statement A particle of mass m is confined (in one dimension) to the region 0 ≤ x ≤ a by a potential which is zero inside the region and infinitely large outside. If the wavefunction at time t = 0 is of the form ψ (x,0) = Ax(a - x) inside the region ψ (x, 0) = 0 outside the...