Mentor note: Thread moved from homework sections as being a better fit in the math technical section.
Multiplying components of both sides are also off limits.
I am trying to derive vector identities on introduction chapters in various EMT books. For example : (AXB).(CXD) = (A.C)(B.D) -...
The overall problem is to prove that [L^2,[L^2,\hat{r}]]=2\hbar^2 {L^2,r}
I feel I am very close to solving this problem but I need a quantum version of the vector identity ax(bxc). Because the relevant vectors are operators that don't commute, there is a problem.
Does anybody know of a source...
1. Okay, so I am going to prove that
\int H_a\cdot H_bdv=0
Hint: Use vector Identities
H is the Magnetic Field and v is the volume.
Homework Equations this this[/B]
k_bH_b=\nabla \times E_b
k_aH_a=\nabla \times E_a
k is the wave vector and E is the electric field
The Attempt at a...
Homework Statement
\displaystyle \frac{d}{dt} (\vec u (t) \vec v (t))= \vec u (t)' \vec v(t)+\vec u(t) \vec v(t)'
I know this is a product rule on the RHS but how does one prove it?
Thanks
I can show that Coulomb's Law + superposition implies \nabla \cdot \mathcal {E} = \frac{\rho}{\epsilon_0} and \nabla \times \mathcal{E} = \mathbf{0}. I want to go the other way and derive Coulomb's law and superposition from the vector identities. I know that Gauss' Law implies Coulomb's law if...
Homework Statement
i have to prove that
∇x(FxG)=(G⋅∇)F-(F⋅∇)G+F(∇⋅G)-G(∇⋅F)
where F and G are vector fields with F=F1,F2,F3 and G=G1,G2,G3 ∇=d/dx,d/dy/d/dz
Homework Equations
The Attempt at a Solution
i have tried applying scalar multiplication and the cross product to...
Homework Statement
Prove using the Levi-Civita Tensor/Kroenecker Delta that:
(AxB)x(CxD) = (A.BxD).C-(A.BxC).D
Homework Equations
εіјkεimn = δjmδkn – δjnδkm (where δij = +1 when i = j and 0 when i ≠ j)
The Attempt at a Solution
if E = (AxB) then Ei = εіјkAjBk, and
if F =...
Homework Statement
Prove the following vector identity:
\nablax(AxB) = (B.\nabla)A - (A.\nabla)B + A(\nabla.B) - B(\nabla.A)
Where A and B are vector fields.
Homework Equations
Curl, divergence, gradient
The Attempt at a Solution
I think I know how to do this: I have to...
Homework Statement
1. Establish the vector identity
\nabla . (B x A) = (\nabla x A).B - A.(\nabla x B)
2. Calculate the partial derivative with respect to x_{k} of the quadratic form A_{rs}x_{r}x_{s} with the A_{rs} all constant, i.e. calculate A_{rs}x_{r}x_{s,k} Homework Equations
The...
Homework Statement
Prove the vector identity: \left(a\times\nabla\right)\bullet\left(u \times v\right)=\left(a \bullet u \right)\left(\nabla \bullet v \right)+\left(v \bullet \nabla \right)\left(a \bullet u \right)-\left(a \bullet v \right)\left(\nabla \bullet u \right)-\left(u...
Homework Statement
Prove using index notation that,
the x denoting a cross-product.
(del x f del g)=del f x del g
Homework Equations
The Attempt at a Solution
dif etc. denote partial derivatives.
RHS=eijkdjfdkg
LHS-I'm not even quite sure how to write it in index...
Vector Identities ??
Having heaps of trouble with v.identities any help possible would be greatly appreciated.
Let F = (z,y,-x) and f = |F| <--- (magnitude F)
Use vector identities to calculate;
\nabla \cdot (f \nabla \times (f F))
Homework Statement
Question One: Prove that |u x v|^2 = (u . u)(v . v)-(u . v)^2 where u and v are vectors.
Question Two: Given that u = sv + tw, prove algebraically that u . v x w = 0 where u, v and w are vectors and s and t are integers.
Homework Equations
I don't know :(
The...
Homework Statement
The vectors F and G are arbitrary functions of position. Starting w/ the relations F x (∇ x G) and G x (∇ x F), obtain the identity
∇(F . G) = (F . ∇)G + (G . ∇)F + F x (∇ x G) + G x (∇ x F)
Homework Equations
The Attempt at a Solution
I started off...