00:01
So, here in this question we are considering about the wave equation that from here is minus of curly square which is divided by the curly of t square plus curly square which is divided by the curly of x square plus k square which is multiplied by the psi of t and x that is equals to zero.
00:17
So, we have to prove or disprove that this wave equation is invariant under lorentz transformation.
00:23
So, here we are considering let's say tx is equals to r beta r beta r r and that from here is t bar and x bar.
00:35
So, this is here where we are considering that the value of r is equals to one which is divided by the under root one minus beta square.
00:44
So, here we are considering that t from here is equals to r of t bar plus beta of r of x bar and we can say that x from here is equals to beta of r of t bar plus r of z bar.
00:56
So, from here the value of curly of t divided by the curly t bar is equals to r and the value of the curly t divided by the curly of x bar that is equals to beta r and the value of curly x divided by the curly t bar is equals to beta of r and the value of curly of x divided by the curly of x bar is equals to r.
01:17
So, from here we can say that curly divided by the curly t is equals to curly t divided by the curly t bar multiplied by the curly divided by the curly t plus curly x divided by the curly t multiplied by the curly divided by the curly x that is equals to r which is multiplied by the curly divided by the curly t plus beta of r that is multiplied by the curly divided by the curly x...