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Homework Statement
I need to find Λ using the equation below (I think).
Homework Equations
A [/B]+ ∇Λ = 0
where A(x,y,z,t) = B[itex]\begin{pmatrix} x+y\\ x-y\\ 0 \end{pmatrix}[/itex]
The Attempt at a Solution
Is this at all possible?
I'm not sure about your notation, is [itex]A[/itex] a matrix, or a vector? Do the three components [itex]x+y, x-y, 0[/itex] correspond to vector components, or matrix components?Homework Statement
I need to find Λ using the equation below (I think).
Homework Equations
A [/B]+ ∇Λ = 0
where A(x,y,z,t) = B[itex]\begin{pmatrix} x+y\\ x-y\\ 0 \end{pmatrix}[/itex]
The Attempt at a Solution
Is this at all possible?
Sorry it is a vector. I was trying to mimic exactly how it is written in front of me.I'm not sure about your notation, is [itex]A[/itex] a matrix, or a vector? Do the three components [itex]x+y, x-y, 0[/itex] correspond to vector components, or matrix components?
Assuming that you mean that [itex]A[/itex] is a vector, then your problem is to find a function [itex]\Lambda(x,y,z)[/itex] such thatI'm not sure about your notation, is [itex]A[/itex] a matrix, or a vector? Do the three components [itex]x+y, x-y, 0[/itex] correspond to vector components, or matrix components?
To solve the equation [itex] \frac{\partial}{\partial x} \Lambda = -B (x + y)[/itex], consider how you would solve the ordinary differential equationAssuming that you mean that [itex]A[/itex] is a vector, then your problem is to find a function [itex]\Lambda(x,y,z)[/itex] such that
[itex]\nabla \Lambda = -A = -B(x+y, x-y, 0)[/itex]
That means that there are three equations for [itex]\Lambda[/itex]:
- [itex] \frac{\partial}{\partial x} \Lambda = -B (x + y)[/itex]
- [itex]\frac{\partial}{\partial y} \Lambda = -B (x - y)[/itex]
- [itex]\frac{\partial}{\partial z} \Lambda = 0[/itex]
Hmm I think I may have to post the question in full. My original post is just a small part of a bigger question (about Gauge transformations) so I am probably going about it wrong.Assuming that you mean that [itex]A[/itex] is a vector, then your problem is to find a function [itex]\Lambda(x,y,z)[/itex] such that
[itex]\nabla \Lambda = -A = -B(x+y, x-y, 0)[/itex]
That means that there are three equations for [itex]\Lambda[/itex]:
- [itex] \frac{\partial}{\partial x} \Lambda = -B (x + y)[/itex]
- [itex]\frac{\partial}{\partial y} \Lambda = -B (x - y)[/itex]
- [itex]\frac{\partial}{\partial z} \Lambda = 0[/itex]
You should always include the full problem as well as your attempts to solve it.Hmm I think I may have to post the question in full. My original post is just a small part of a bigger question (about Gauge transformations) so I am probably going about it wrong.