(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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?

2. Relevant equations

3. 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?

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# Homework Help: 4 vector problem

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