Homework Statement
Show that the anticommutator of parity and boost is zero.
Homework Equations
\{\mathcal{P},K^{i}\}=0
The Attempt at a Solution
Let the anti commutator act on a state
\{\mathcal{P},K^{i}\}\Psi(t,\vec{x})=\mathcal{P}K^{i}\Psi(t,\vec{x})+K^{i}\mathcal{P}\Psi(t,\vec{x})...
I understand the idea behind the optical interference that produces colors on thin films but have never figured out the reason that the films have to by 'thin'. What is the lack of similarity that I am missing between a film and a somewhat thick sheet of glass or something that makes these...
I've got three questions basically.
Do photons actually have only an integer spin +/- 1, or do people really only mean the sign of its chirality? The reason I ask is that I am interested in whether the photon spin is related to its frequency. This leads to the next question.
Is the basis for...
I have been trying to figure this out for a couple weeks now. Why does the Legendre transform require that the function be convex?
Is it because g(x) has to be solved to get x(g) and finding this inverse means g(x) should be bijective? (And if g is bijective then dg/dx will always be positive...
I have seen this sort of thing over the past few years and it is bothering me, something like this
\frac{ds}{dx}=\frac{1}{\frac{dx}{ds}}
But it seems to me that this sort of thing only works in certain situations. For example, take s(x) to be
s(x)=x^{2}
so that
\frac{ds}{dx}=2x
Now to get...
I am very early into my first look at topology (specifically, I am jumping to topology on smooth manifolds through the Baez/Muniain book - Gauge Fields, Knots and Gravity) and I have a few questions. Suppose we have overlapping sets on a manifold A and B like this...
I have heard (what I consider to be) a myth of a pole lifting off the ground before it hits. That is, set something like a telephone pole up on end with no initial falling velocity, then let it drop. The claim is that the bottom of the pole actually lifts from the ground before the whole thing...
I am trying to understand the definition of the inner product of two functions on an interval. I know that the form of a scalar product in finite dimensional space is given by
\vec{\phi} \bullet \vec{\psi}= \sum_{k} \phi_{k} \psi_{k}
and in infinite dimensional space
\langle \phi , \psi...
I am reading both Griffiths and Gasiorowicz and I can't get either of them to tell me why the continuity of the derivative of the natural log of the amplitude
\frac{d(ln(u(x)))}{dx}=\frac{1}{u(x)}\frac{du(x)}{dx}
or put a different way
\frac{1}{u(a^{-})}\frac{du(a^{-})}{dx}=...
Homework Statement
Suppose that u(x,y) is a solution of Laplace's equation. If theta is a fixed real number and v(x,y)=u(xcos\theta-ysin\theta,xsin\theta+ycos\theta)
show that v is a solution also.
Homework Equations
\nabla^{2}u(x,y)=0
The Attempt at a Solution
To be honest I haven't...
Homework Statement
A photon whose energy equals the rest energy of the electron undergoes a Compton collision with an electron if the electron moves off at an angle of 40 degrees with the original photon direction, what is the energy of the scattered photon.
Homework Equations
E2 = (m0c2)2...
Homework Statement
Show that the total time derivative wrt time of this function
S=-k\int_{r} \int_{v}f \ln(f)d^{3}vd^{3}r
vanishes.
Homework Equations
\frac{DS}{Dt}=\frac{\partial S}{\partial t}+\vec{v} \bullet \nabla S+ \vec{a}\bullet\nabla_{v}S
where \nabla_{v} is the gradient in...
I keep seeing this equation pop up and I have no idea what it is or where it comes from.
n_{1}f_{1}= -n_{2}f_{2}
It looks like a take on snell's law, but what assumptions have to be made to get to this equation from snell's?
I am stuck in trying to understand the derivation of the Euler-Lagrange equation. This mathematical move is really bothering me, I can't figure out why it is true.
\frac{\partial f(y,y';x)}{\partial\alpha}=\frac{\partial f}{\partial y}\frac{\partial y}{\partial\alpha}+\frac{\partial...
I have been searching for a way to relate known concepts (known to me) to the computation of the dot product in an effort to understand why it takes the form it does. I ran into a little snippet in a classical dynamics book that seems like it just may be the ticket.
Here is what it says...
Homework Statement
A pair of infinite, parallel planes are equipotential surfaces. The plane at z = 0 has an electric potential of 0 and the plane at z = b also has a potential of zero. The electric field at b is 0 at time t at which there is a constant, positive charge density between the...
I saw the argument for complex differentiation today and I had a question about a 'well known' aspect of the argument. My professor said something like this (at least a version of it): Derivatives on complex variables are defined in the usual way. However, in the complex plane, delta(z) may...
I'm trying to wrap my brain around the notion of tunneling and am hoping somebody could be of assistance.
I'm wondering about the history of the idea, why was the notion of quantum tunneling first created? (What prompted the idea?)
Also, I'd like to find experiments that have shown that...
Homework Statement
For F = (x, y2, 2z), evaluate the path integrals along the line of a to b:
\vec{a}=(0,0,0), \vec{b}=(1,1,1), \int^{b}_{a} \vec{F} \times d\vec{r}
\int^{b}_{a} \vec{F} ds
Homework Equations
No idea.
The Attempt at a Solution
I don't have a clue what these...
I have some questions about the TNB frame.
The T unit vector is defined this way:
\hat{T} = \frac{dr(t)/dt}{ds/dt} = \frac{dr(s(t))}{ds}
So, it is parametrized by arc length. Why can't t be left as the parameter? Is this just for definition-of-curvature-sake? If so is there any reason...
Homework Statement
Show that, regardless of its initial energy, a photon cannot undergo compton scattering through an angle of more than 60 degrees and still be able to produce an electron positron pair. (Hint: Start by expressing the Compton wavelength of the electron in terms of the...
In a table in two different books they both say:
\int \frac{1}{a^2-u^2}du=\frac{1}{2a} ln\left|\frac{u+a}{u-a}\right|+c
but I am not having the same result:
\int \frac{1}{a^2-u^2}du=\frac{1}{2a} \left(\int \frac{1}{a-u}du + \int \frac{1}{a+u}du\right) = \frac{1}{2a} \left(-ln\left| a-u...
Homework Statement
Problem given basically in the beginning of the book, Sec. 1.4, about separable equations.
Find general solutions (implicit if necessary, explicit if convenient) of the diff. eq.
dy/dx+2xy^2=0
Homework Equations
There was a previous section where they popped...
Homework Statement
\int \frac{x}{x+d}dx
The Attempt at a Solution
I tried parts and that turned out horribly so I fired up maple. First move it makes is 'Rewrite Rule'. I've never heard of a rewrite rule but I supposed it could be some algebraic massaging. I ended up looking at it...
Homework Statement
A pyramid with horizontal square base, 6.00 m on each side, and a height of 4.00 m is placed in a vertical electric field of 52.0 N/C. Calculate the total electric flux through the pyramid's slanted surfaces.
Homework Equations
Electric Flux = E dot dA
The...
I am not sure exactly what is happening between the first part and second part. What happens to the 2?
Also, what technique do you use to integrate after that? I am a little unsure as to what slick moves are being used here. Any help is appreciated...