Recent content by Shing

Thanks for telling me! I am all ears :)

I was thinking of a Fermi-question: the thickness of atmosphere with diffusive equilibrium. And I estimated roughly 10^{5}m (where it should be ~10^{4}m). The difference of order of magnitude to real thickness is 1 (from Wiki). I had a lot of fun, and I am looking for interesting ways other...

Usually with extremely high focus, one can finish one undergraduate course on his own for about one month (especially we have open course, physics forum, stackexchange, etc now) So why don't you do this in your summer break instead? say, do some reading on Apostol's Calculus (assuming you have...

I know :( but I think mostly due to other physicist, especailly Mach's prejudge and criticisms toward him

Thanks :) Is it okay for you to tell me if she receiving any medical treatment? Whenever I take pill, my mind runs slowly comparing with "normal" state and have a hard time focusing on thinking... :(

Thank you for your reply :) there was a senior real brilliant on physics has a bipolar disorder too, I will go to ask his suggestions. (though there seems to be many sub-types of bipolar disoder And my recent doctor pretty cares about me, I feel so warm around her. And bipolar disorder is one...

Thank you so much for your advice :) I have a doctor appointment once every other week. (she is good and inspiring) The real hardship is my way studies is: 1.)I can be creative and original, but I must study at a low speed (even with bipolar disorder, because simply being creative means a...

I am a year three who suffer badly from bipolar disorder II, it damages me both school grades and communication skills (and honestly speaking, not training myself on these things, I have been only doing only what I want, not what I need, bad idea) . nevertheless, I like nature, I spent far...

Now I got it a bit! For column vector (1,0) -> (0 ,1) And T is {(0,1),(1,0)} :) Did I get it right?

Thanks for reply, So here is my understanding: we map A to B, A and B represent the same thing in different bases, and their mathematical relation is A=T^{-1}AT am I right? I have a rough picture now, but Sadly, I still can't see the physical picture, neither the mathematics. , and shanker...

Forgive my ignorance, But shouldn't "unaffected by a unitary change of basis" be expressed asTrUΩ=TrΩ

Homework Statement Shanker 1.7.1 3.)Show that the trace of an operator is unaffected by a unitary change of basis (Equivalently, show TrΩ=TrU^{\dagger}ΩUHomework Equations I can show that via Shanker's hint, but I however can't see how a unitary change of basis links to TrΩ=TrU^{\dagger}ΩU...

Thank you so much for your reply, I am sorry that I can't understand it completely (since English is my 2nd language) so my understanding is: A vector with complex structure can be thought of a arrow(vector itself) with feathers (the complex number stays with the vector). While arrow...

Would anyone be kind enough shed some light on the physics Intuition of a vector in a linear space over a complex field for me? Furthermore, what does z^z mean?

You guys are my heros!