The reason I ask the aforementioned question is because I came across the expectation values of operators in Quantum Mechanics. And part of the computation involves integrating a function of the complex conjugate of x with respect to dx.
So as an example let's say I have:
∫ sin (x*) dx where...
I've been trying to calculate the Riemann Curvature Tensor for a certain manifold in 3-dimensional Euclidean Space using Christoffel Symbols of the second kind, and so far everything has gone well however...
It is extremely tedious and takes a very long time; there is also a high probability...
The substitution would certainly be effective in solving the integral.
If you make the substitution u=sint, then du=cost dx, so 1/(cost) du = dx
Therefore the integral simplifies to integrating (u+3i)^(-2) du.
Thank you Vargo, I think I fully grasp the concept of the metric tensor now. However I still have some concerns with regards to the curvature tensor, but I think they will dissipate once I've done some problems (and begin to compute them). Thank you very much.
Yes, Guillefix. I used different coordinate systems (ergo the position vector had different components when using i,j and k unit vectors) but all in Euclidean Space.
I have looked at the definition of the metric tensor, and my sources state that to calculate it, one must first calculate the components of the position vector and compute it's Jacobian. The metric tensor is then the transpose of the Jacobian multiplied by the Jacobian.
My problem with this...