Wave function simplification in relativistic coordinates?

[sciencegem]

My textbook says
ψ(x,t)=exp(i(p[itex]_{0}[/itex]x[itex]^{0}[/itex] + p[itex]^{→}[/itex][itex]\cdot[/itex]x[itex]^{→}[/itex])/h)=exp(i*p[itex]\cdot[/itex]x/h)
(note that by h I mean 'h-bar'...couldn't find the symbol).
I don't recognize (like my text implies I should) how the first equation equals the second. Where did the p[itex]_{0}[/itex]x[itex]^{0}[/itex] go? Sorry for my stupidity here. Any hints appreciated. Thanks.

 

[jtbell]

On the right side, he's considering p and x as relativistic 4-vectors. p⋅x is the 4-vector "dot product" which is defined as the expression in the inner parentheses on the left side.

 

[sciencegem]

On the right side, he's considering p and x as relativistic 4-vectors. p⋅x is the 4-vector "dot product" which is defined as the expression in the inner parentheses on the left side.

I can't believe I didn't think of that. Thank you!

 

[Bill_K]

(note that by h I mean 'h-bar'...couldn't find the symbol).

In TeX it's \ hbar. In UTF it's just ħ

 

[sciencegem]

Thanks!