- #1

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Given: [tex] m\frac{d^{2}x^{\mu}} {d\tau^{2}} =e{F^{\mu}_{nu}} \frac{dx^{\nu}} {d\tau}[/tex]

I have to define [tex]u^{\mu}= \frac {dx^{\mu}} {d\tau^2}[/tex]

and obtain:

[tex]u^0= cosh(\frac {eE\tau} {m}) u^0(0)+ sinh(\frac {eE\tau} {m})u^1(0) [/tex]

[tex]u^1= sinh(\frac {eE\tau} {m}) u^0(0)+ cosh(\frac {eE\tau} {m})u^1(0) [/tex]

I don't understand what I should do. First, what does u(0) mean? u(x=0)? how do I obtain these equations?

What is the relation between [tex] x^{\mu} [/tex] and [tex] x^{\nu} [/tex]?

If I define this four vector, u, and u refers to mu, than what am I to do with the other index, nu?

Thank you! I have been struggling for two days...

Noam