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1. The heuristic understanding of polarization operator?

I find that some book e.g. Many-body theory of solids by John C. Inkson P145 says that :" By analogy with the classical polarization, we define a polarization propagator through the relationship ... ε=1-vP" , where ε is the dielectronic response function, and v is the bare Coulomb...
2. Need help with quantum open system!

Sorry, I have not provided enough information. In fact, nanoelectronics or moluclar electronics calls for time dependent density functional theory combined with non equilibrium Green's function.
3. Need help with quantum open system!

Hello everyone, I am a student major in physical chemistry, but my PhD supervisor ask me to do some theoretical research in the field of quantum open system i.e. quantum transport. I feel it beyond my reach. I've learned that the this field belongs to non equilibrium quantum statistical...
4. An integral inequality

In fact, yes! But what I'm really eager to know is how to prove the conclusion. Maybe when the x is large enough, [∫f(t)dt]^2 is larger.
5. An integral inequality

Homework Statement suppose f(x) is monotonely decreasing and positive on [2,+∞), please compare [∫f(t)dt]^2 and ∫[f(t)]^2dt, here "∫ "means integrating on the interval [2,x] Homework Equations none The Attempt at a Solution Maybe the second mean value thereom of integral is helpful.

Thanks. but I still have some problems. I can't show that If {a_n} contains an infinity of distinct element, the sequence is convergent and converges to v. Is the set S bounded?

Homework Statement Serge Lang Undergraduate Analysis Chapter Ⅷ §1 Exe4 Let{Xn} be a sequence in a normed vector space E such that {Xn} converges to v. Let S be the set consisting of all v and Xn. Show that S is compact. Homework Equations None The Attempt at a Solution I guess that...
8. An inequality about inner product

Oh,my god!I found a severe mistake. We can't claim that Abs(C)Abs(B) = Abs(A-C)Abs(B) - Abs(A)Abs(B) Abs(A)Abs(C) = Abs(B-C)Abs(A) - Abs(B)Abs(A) So, I'm very sorry to say that we didn't verify the inequality.
9. An inequality about inner product

Thanks very much! Note that 2Abs(A)Abs(B)>=0, so Abs(A-C)Abs(B) + Abs(B-C)Abs(A) - 2Abs(A)Abs(B) <= Abs(A-C)Abs(B) + Abs(B-C)Abs(A) thus, Abs(A-B)Abs(C) <= Abs(A-C)Abs(B) + Abs(B-C)Abs(A) - 2Abs(A)Abs(B) <= Abs(A-C)Abs(B) + Abs(B-C)Abs(A). It's obvious that if A=B=C the equal mark holds...
10. An inequality about inner product

If α,β,γ are vectors in the Euclid space V, please show that |α-β||γ|≤|α-γ||β|+|β-γ||α|,where |α|=√(α,α) and point out when the equal mark holds. Can someone help me out?
11. A difficult problem about linear algebra.Help

A difficult problem about linear algebra.Help! Suppose that A is a m*n matrix，B is a n*m matrix,and AB is a idempotent matrix. Please verify that BA is also a idempotent matrix.
12. A problem in Hoffman's Linear Algebra

How about the Inversion of the proposition?
13. A problem in Hoffman's Linear Algebra

A problem in Hoffman's Linear Algebra. Page 243 18. If T is a diagonalizable linear operator, then every T-invariant subspace has a complementary T-invariant subspace. And vice versa. In fact, the answer lies on Pages 263~265,but I try not to use the conception T-admissible to prove this...