- #1
neelakash
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Homework Statement
I cannot remember if I have already posted this question here...
However,if that is the case,let it be said that I want to discuss more about it.
Let us define 4 vector by 4 co-ordinates (x1,x2,x3,x4) where (x1,x2,x3) are space components (like x,y,z) and x4 is related to time as x4=ict.Express the following equations in tensor notation.
(i)The continuity equation: div J+(del*rho/del t)=0
(ii)The wave equation del2ø-(1/c2) [del2 ø/del t2]=0
(iii)What will be the value of j4 instead of above?
Homework Equations
The Attempt at a Solution
For the first two part I am getting these:
Please check...
Let me know if I am correct.
(i) (∂/∂x_i)(J_i)+ (∂/∂t)ρ=0
(ii) [∂^2/(∂x_i*∂x_i)]ψ-(1/c^2)[(∂^2/∂t^2)ψ]=0
I have changed phi to psi...
Do not mind.
How can I get the 3rd part?