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4

For many materials the change in refractive index over the range of visible wavelengths isn't huge, so it's not a bad approximation to take a single value. The range of visible wavelengths is from about 400nm to 700nm, so the middle wavelength is 550nm. As it happens, the sodium D lines are not far from this, at 589nm, and since they are bright and easy to ...


1

In mechanics, a mass $m$ experiences a force $\textbf{F}$ along some path $C$. The work done on the mass is given by $$ W = \int_C \textbf{F} \cdot d\textbf{r},$$ such that the energy of the mass increases by $W$. Positive work corresponds to energy being added to the system in question (which is inevitably taken from the surroundings). Edit: To answer ...


4

The upshot is that we need one condition to specify how the operators in the Schrödinger and Heisenberg picture are connected. This is usually done by declaring that the two pictures agree at some fixed instant $t_0$. To summarize: The Schrödinger operator $\phi(\textbf{x},t_0)$ does not depend on time $t$, while the Heisenberg operator ...


4

Kelvin is the SI unit. It is far more common than Rankine. I cannot recall ever encountering Rankine temperature units, except in historical or humorously-backward contexts. Note that these measure temperature, not heat. The SI and "imperial" measures of heat is are the joule and the BTU, respectively. To avoid causing headaches, use SI for everything — ...


6

The four-potential is not an observable because it is not invariant under a change of gauge. And no predictions of any physical theory are dependent on the choice of gauge, so the four-potential is not observable. What is gauge invariant and observable is the integral of the four potential around a loop, and that is what is observed in the AB effect. ...


3

Well, if you're wondering if people won't know what it is, or if you should be calling it something fancier: no. This and closely related notions are common language among physicists, much like "mass" and "force" are common language. A "right-handed triple" is a collection of three vectors in a particular order such that they obey the right-hand rule. A ...


4

If you stick to one convention out of many other conventions, you should have same results regardless of signature of metric. Here I follow Carroll's conventions: http://amzn.com/0805387323. For Christoffel symbol, we have \begin{equation} \Gamma^\lambda_{\mu\nu}=\frac{1}{2}g^{\lambda\rho}(\partial_\mu g_{\nu\rho}+\partial_\nu g_{\rho\mu}-\partial_\rho ...


1

The signature is one convention (both in special relativity and in general relativity). But in general relativity there are many different conventions besides just the signature. The front inside cover of Misner Thorne and Wheeler lists conventions for signature, for the Riemann Tensor, for the Einstein Tensor, and for the use of Greek and Latin indices and ...


3

If the resultant force acting in a body is give by minus the gradient of potencial you can show that $\frac{dE}{dt} = 0$. Where E is the total energy of particle. So total energy, kinect + potencial is conserved. In 1-dimensional case: $\frac{dE}{dt}=\frac{d(\frac{1}{2}mv^2+V(x))}{dt}=mv\dot{v}+\frac{dV}{dx}\frac{dx}{dt}$ $=v(ma + \frac{dV}{dx})$


8

We introduce a minus sign to equate the mathematical concept of a potential with the physical concept of potential energy. Take the gravitational field, for example, which we approximate as being constant near the surface of Earth. The force field can then be described by $\vec{F}(x,y,z)=-mg\hat{e_z}$, taking the up/down direction to be the $z$ direction. ...


1

Both negative sign and positive sign are correct. When you make an infinitesimal rotation with angle $d\phi$ about the z-axis, then both two following representations for transformed coordinates are true: $$ \left\{ \begin{array}{ll} x'=x-d\phi y \\ y'=y+d\phi x \end{array} \right. $$ and $$ \left\{ \begin{array}{ll} x'=x+d\phi y \\ y'=y-d\phi x \end{array} ...


2

Comments to the question (v3): Recall that the restricted Lorentz group $$\tag{1} SO^+(3,1)~\cong~ SL(2,\mathbb{C})/\mathbb{Z}_2$$ is locally isomorphic to the Lie group of complex $2\times 2$ matrices with unit determinant, cf. e.g. my Phys.SE answer here. The Lie group of 3D rotations $$\tag{2} SO(3)~\cong~ SU(2)/\mathbb{Z}_2$$ is a subgroup thereof. The ...



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