Recent content by cin-bura

hello! Does anybody know the physical justification of the de broglie relation p=\hbar k? or (i guess equivalently) for p=-i\hbar ∂/∂x ? i came across a more general "law" in laser physics, where momentum is seen as the gradient of the phase of a scalar light field (used in eg the paraxial...

all right, i think i got it now thank you everyone!

well, as you said: r =\sqrt{x^2+y^2} = \sqrt{1/2+1/2} = 1 θ = arctan(y/x) = arctan(\frac{\sqrt{2}}{\sqrt{2}})=\frac{\pi}{4} it represents a vector with magnitude 1 pointing in 45° direction

you are perfectly right. i did not write Ã(u) in terms of the polar basis. also, it should be \frac{\partial x}{\partial r} = cos(\phi) \frac{\partial x}{\partial \phi} = -r sin(\phi) but what about the non symmetrical case? consider a map that assigns a constant vector to every...

thank you for your vivid explanation! i really do see clearer now. i think the point i missed in the example was that Ã(u) not only depends on u but is also expressed in the u coordinates. cheers

thank you for your replies! i think that it is valid at each point is a very valuable statement. still, i am not completely clear about that: doesn't the definition of a derivative require an infinitesimal displacement away from this point? to show more clearly what i mean, here is an...

hello! i am having a hard time understanding this: contravariance is defined in the textbooks as some entity that transforms like \tilde A^{\mu}(u)= \frac{\partial u^{\mu}}{\partial x^{\nu}} A^{\nu}(x). du/dx is not constant in space because the relations between 2 coordinate systems don't...