cragar
- 2,546
- 3
This is not a homework problem, just trying to figure out what shankar did.
[itex]U|u_i>=u_i|u_i>[/itex]
[itex]U|u_j>=u_j|u_j>[/itex]
Ok so we have these 2 equations and then shankars says to take the adjoint
of the second equation and dot each side with the corresponding side of the first equation,
we get
[itex]<u_j|U^tU|u_i=u_i{u_j}^*<u_j|u_i>[/itex]
is the [itex]{u_j}^*[/itex] just the complex conjugate of [itex]u_j[/itex] ?
Now that I typed it out it seems more clear I originally thought there was an extra factor.
[itex]U|u_i>=u_i|u_i>[/itex]
[itex]U|u_j>=u_j|u_j>[/itex]
Ok so we have these 2 equations and then shankars says to take the adjoint
of the second equation and dot each side with the corresponding side of the first equation,
we get
[itex]<u_j|U^tU|u_i=u_i{u_j}^*<u_j|u_i>[/itex]
is the [itex]{u_j}^*[/itex] just the complex conjugate of [itex]u_j[/itex] ?
Now that I typed it out it seems more clear I originally thought there was an extra factor.