Recent content by Chillguy

If we know the reciprocal space basis of a BCC lattice b_1=\frac{2\pi}{a}(\vec{x}+\vec{y}),b_2=\frac{2\pi}{a}(\vec{z}+\vec{y}),b_3=\frac{2\pi}{a}(\vec{x}+\vec{z}) how do we go about finding the shortest reciprocal lattice vector and its corresponding miller index? To me all the constants in...

What is the information given about the movement, only that it is moving left?

How fast does the problem state that the boat is moving, which direction is it moving in, is the boat only moving in the latter parts of the problem? In your original post you only state the length/mass of boat and position of the man/his mass relative to the boat, it seems some information is...

http://en.wikipedia.org/wiki/Table_of_spherical_harmonics

Hey, I think you will want to double check your answers. Without doing any calculations you can see something is off; considering the man moves position between part 1 and 2 yet the location of center of mass stays the same according to what you have written? Is the boat moving for part 3...

Homework Statement Prove that the lattice planes with the greatest densities of points are the {111} planes in a fcc bravis lattice and the {110} planes in a bcc bravis lattice.Homework Equations d/v=points per unit area where d is the spacing of planes and v is the unit volume.The Attempt at a...

Homework Statement Let T be the unique linear operator on C3 for which T_{\epsilon1}=(1,0,i), T_{\epsilon2}=(0,1,1), T_{\epsilon3}=(i,1,0). Is T invertible? 2. Homework Equations If we show T is non singular or T is onto, then this would imply T is invertible. The Attempt at a Solution I...

Yes! it does! Thank you so much. It makes much more sense now. I just have one other question, why do the vectors need to span all of R^3 in the first place? Is it so the transformation can go to any place in R^2?

T(v)=T(c*v_1+c*v_2+c*v_3) Which I can then apply the definition of a linear transformation as defined before?

The resulting combination will be a vector in R^2, I think it could be any vector in R^2?

... can be written as T(c\alpha_i+\beta_i)? where alpha and beta are vectors in R3

It would allow me to span R3 with these three vectors

Homework Statement From Hoffman and Kunze: Is there a linear transformation T from R^3 to R^2 such that T(1,-1,1)=(1,0) and T(1,1,1)=(0,1)?Homework Equations T(c\alpha+\beta)=cT(\alpha)+T(\beta) The Attempt at a Solution I don't really understand how to prove that there is a linear...