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• Users: tghg
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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.
6. ### A problem about compactness

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?
7. ### A problem about compactness

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...