Recent content by easttiger2007

in the simple case of a particle of mass m in Cartesian coordinates, the Hamiltonian function of motion is \(\emph{H}(\textbf{r,p})=\frac{1}{2m}(p^{2}_{x}+p^{2}_{y}+p^{2}_{z})+\emph{V}(x,y,z)\) The relations mentioned previously can be derived: \(\frac{\partial x}{\partial...

If my knowledge is correct, the de Broglie hypothesis is part of the foundation of Schrödinger's equation. Logically, it is the cause of those "physical effect" via the Schrödinger's equation, but I think the original question of this thread is for the cause of this hypothesis, and that is just...

I recommend A.P.French's book, Feynman's lecture, and Einstein's Meaning of Relativity. But for taking Physics Olympiad, the most efficient way is to work on problems. I recommend you to find some Chinese Physics Olympiad Problems (if english version is available), or Russian, Polish, etc. btw...

My point is that it's just mathematical postulation. But it works well in accounting for the real-world phenomena. Like in the sun, the "light pressure", which is from the exchange of light's momentum, prevents it from collapse due to gravitation.

In a mathematical view, it's just a postulation proposed by de Broglie. Later physical experiment had proved that wave could interact with particle and de Broglie's postulation accords with the basic conservation principles. It then became one of the cornerstones of quantum mechanics and works...

Maybe you'd also consult some book in differential geometry. The negative sign has induced people to consider the basic definition of the product of two infinitesimal quantities.

I think divergence theorem require a domain that has "boundary", which is necessary for a "compact domain". Basically, divergence thm, along with the 1D Newton-Leibniz version, and the 2D Stoke's version, can be regarded as the basic thm of calculus in the first 3 dimensions. They apparently...

I think a lot of math need to be done to answer your question. But qualitatively, if you take into account that light behaves like particle and abide by the mechanical equation of collision, and treat the surface atoms of the reflection material as rigid balls, you will get it quickly, though...

The discussion goes too far. The question is simple, but need to be clarified by classifying into following two cases. Case 1. Just the NSL changes its form, say f=m^2*a or or f=sin(m)*a etc. This will be a problem of mathematical deduction. Case 2. Inertia just vanish completely. Then it can be...

Change in temperature will lead to change in density(rho) and depth(h). but rho=m/V=m/(S*h) or rho*h=m/S. If S is fixed, then change in temperature will not affect the pressure, if S is not fixed, then it depends on the shape of the container.