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...
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.
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...
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...
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.
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?
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.
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...