To my understanding, QED is about electromagnetic interaction, and in a solid system, the interaction is only electromagnetic
So why there are stills lots of research in solid state physics ? Is there something not explained by QED ?
I would like to learn topological insulator. But what kind of reference should I look for.
I just have some basic solid state physics knowledge.
I know there are lots of Hall Effects (e.g. spin hall effect, quantum hall effect ...etc). and I just know the idea of them, but not the math
I am learning some basic solid state physics idea, like density of state ...etc.
For particle in a 1D box,
E = n^2 (pi)^2 (h_bar)^2 / 2mL^2
But why it is written as
E = (h_bar)^2 k^2 /2m
does it means that energy eigenvalue E is related to momentum k ?
I guess it is not because momentum is...
I am reading some papers about astroparticle physics and I see something like Parker limit (monopole).
So what is the purpose of setting up this limit ? It is be used to get the expected number of particles per unit area per unit time for later experiments ?
Thanks
I got some questions about QM (not well organized)
There is wave-particle duality. To my understanding, particle can behave as billard ball and wave.
Is the wave property means that we can represent the particle by wavefunction ?
The modulus of wavefunction in Schrodinger equation is...
Suppose a point charge is accelerating uniformly. It emits EM radiation.
If an observer is co-moving with the point charge, the point charge remains at rest in his/her frame.
So I guess it does not radiate relative to the co-moving frame.
But someone told me that acceleration is absolute...
I read some of the articles related to particle physics experiment and don't know the meaning of it.
1. minimum bias event
2. pile up
Also, η (pseudo-rapidity) is used instead of θ to describes the angular distribution, but why ?
Can someone explains to me ?
To find a new particle, the energy and momentum of the (decayed) particles are measured
Evaluate the expression m^2 = E^2 - p^2 and plot a histogram.
I just don't understand why there is a resonance particle if there is a peak in the histogram.
Is it because the probability is very high...
From wikipedia, differentiate mv with respect to time by product rule gives wrong result.
It claims that F = dp/dt can only be used in closed system.
http://en.wikipedia.org/wiki/Newton_second_law#Variable-mass_systems
So, there is a non conservative force in this problem.
if I am able to formulate the new "potential", is it still possible to use Lagrangian formulation ?
From (Marion 5th ed. Problem 9-15)
A smooth rope is placed above a hole in a table. One end of the rope falls through the hole at t = 0, pulling steadily on the remainder of the rope. Find the velocity and acceleration of the rope as a function of the distance to the end of the rope x...
In classical mechanics, we say angular momentum is conserved when its magnitude and direction are constant for all time.
But in quantum mechanics, the direction of angular momentum is uncertain.
So, can I say its direction is changing all the time ??
You can try the method "seperation of variable"
For simplicity, we stick in 1-D
Step 1 let ψ(x,t) = X(x)T(t)
now the equation(PDE) becomes ODE (second order)
Step 2 divide both sides by X(x)T(t)
then you should get LHS(depends on t only) = RHS(depends on x only)...
In a central force problem,
angular momentum is conserved.
we quantized one of the component of L, say Lz.
Also, we quantized the angular momentum, L = √l(l+1)h_bar
If we know Lx and Ly without uncertainty,
then we know the direction of L.
Hence we know the motion of the particle is...
Question
Particle in a box (2D)
Determine the energy levels (degeneracy) of the lowest three
I found that E = A (4a^2 + b^2)
where A is a constant
a and b are positive integers (principle quantum number)
My steps
I assume 4a^2 + b^2 = k
where k is also a positive integer...
If I have an infinitely large conductor plate with uniform charge density.
E = σ/2ε (suppose it is in x direction)
V = -∫E dx (from x0 to x)
V = -(σ/2ε)(x - x0 )
From this expression, I can't choose reference at infinity (i.e. x0 --> infinity) because the whole expression V would be...
What is the criteria in choosing infinity as zero potential ?
e.g. an infinite plate with uniform charge density.
What is the physical meaning of not be able to choose a position as reference potential ??
Solving infinite rod, full Fourier transform(complex form) is used in my note.
But the (natural) boundary conditions are even, should I use cosine transform ?
When the rod is infinite or semi-infinite, I was taught to use Fourier transform.
But I don't know when should the full Fourier transform or sine/cosine transform be used.
how's the B.C. related to the choice of the transform ?
Problem
Find the minimum energy of the hydrogen atom by using uncertainty principle
a. Take the uncertainty of the position Δr of the electron to be approximately equal to r
b. Approximate the momentum p of the electron as Δp
c. Treat the atom as a 1-D system
My step
1. Δr Δp ≥...
Given two vectors
x(t) = (e^t te^t)^T
y(t) = (1 t)^T
a) Show that x and y are linearly dependent at each point in the interval [0, 1]
b) Show that x and y are linearly independent on [0, 1]
I compute det([x y]) = 0, so they are linearly dependent
how about part b. Isn't a)...
I also find something strange
using the same condition as stated in the picture (see #3)
Faraday's law in integral form
∫E dl = 0 for any closed loop, so E must be 0
Faraday's law in differential form
curl E = 0, does not imply E = 0
self contradictory ??
or Faraday's law is...
From the diagram
Lorentz force(radial component) drives the charge carrier (e.g. +q) to the centre of the disk, leaving negative charge on the rim.
so there is electric field, which is conservative inside the disk
Hence emf is built up from the centre to the rim of the disk...
Wire A and B, which have the same cross-sectional area are connected in series. There is a p.d. V across the whole wire.
Suppose the two wires obey Ohm's law J = σE
Also, A and B have different conductivity.
Therefore electric field of A is different from B.
There should be a layer of...
A conducting disk is rotating under a uniform magnetic field.
Using Lorentz force F = qv x B, we can conclude that emf produced.
Using Faraday's law, ∫E dl = 0 for any closed loops since there is no magnetic flux change.
So E = 0.
Contradiction ?
If I choose the system to be the box only, I observe that the momentum of the box is decreasing.
So the box should experience a net force. But there is none.
why?
A box which carries sand is moving with a constant velocity u on a smooth horizontal surface.
The sand is removed during the motion of the box such that the sand has the same horizontal velocity u.
We know that there is no horizontal force exerts on the box.
The box will travels in...