Recent content by LayMuon

Doesn't evaluate the first one.

How can I find an Integral of an exponential with Polynomial argument with finite limits: \int_0^\pi \exp^{-a x^2 -b x^4} dx \\ \int_0^\pi \exp^{-a x^2 -b x^4} (x - x^3)dx

Hi Guys, I read that the Fermi level of semiconductor, like germanium, is in-between the completely occupied upper band and conduction band, i.e. right in the gap. Why is that? shouldn't it have beed exactly the highest occupied level ?

Hi guys, I am not economist, but can anybody tell me whether there is a mathematical model for growth in free market economy without state intervention? Where can I look them up? Thanks.

I still don't understand. They are different parts of lorentz matrix. One can only use the definition of lorentz group, I.e. orthogonality.

How did you get this: ( A^{ 0 }{}_{ i } )^{ 2 } = ( A^{ 0 }{}_{ 0 } )^{ 2 } - 1 ? I understand it for B. how are A^0{}_j and A^j{}_0 related?

Yes, that's clear.

|C^0 {}_0 - A^0 {}_0 B^0 {}_0 | \leq \sqrt{\sum_i(1-B^0{}_0{}^2)}\sqrt{\sum_j(A^0{}_i)^2} . I don't know how to express $$ A^0{}_i^2$$ in terms of A00

So how does it work out?

Thanks for reply. Why is there a minus sign in Schwartz inequality? Isn't it \sqrt{ ( A^{ 0 }{}_{ i } )^{ 2 } ( B^{ i }{}_{ 0 } )^{ 2 } } \geq |A^{ 0 }{}_{ i } \ B^{ i }{}_{ 0 }| ? C^0 {}_0 - A^0 {}_0 B^0 {}_0 = A^{ 0 }{}_{ i } \ B^{ i }{}_{ 0 } How to proceed?

\Lambda^0_0 \geq 1

In a Lorentz group we say there is a proper orthochronous subspace. How can I prove that the product of two orthchronous Lorentz matrices is orthochronous? Thanks. Would appreciate clear proofs.

That all was implied. The question is why should we take the self energy density of the magnetic field as H^2/2 and not B^2/2 , unlike the electric field where it is E^2/2 and not D^2/2 .

The total energy of the magnetic field in the matter is \frac{\mu H^2}{2} , I want to calculated the energy that is being spent as a the work on magnetizing the material, so I need to subtract the energy of the magnetic field itself \frac{B^2}{2} and the dipolar interaction -\vec{M} \cdot...

thanks.