In the physical sciences, a particle (or corpuscule in older texts) is a small localized object to which can be ascribed several physical or chemical properties such as volume, density or mass. They vary greatly in size or quantity, from subatomic particles like the electron, to microscopic particles like atoms and molecules, to macroscopic particles like powders and other granular materials. Particles can also be used to create scientific models of even larger objects depending on their density, such as humans moving in a crowd or celestial bodies in motion.
The term 'particle' is rather general in meaning, and is refined as needed by various scientific fields. Anything that is composed of particles may be referred to as being particulate. However, the noun 'particulate' is most frequently used to refer to pollutants in the Earth's atmosphere, which are a suspension of unconnected particles, rather than a connected particle aggregation.
What would it look like if I used a particle accelerator to remove a proton from a particular element? What would the physical change in the element look like if observed? Would the element appear to "magically" change into something else right before your very eyes, as if by some kind of spooky...
There are 36 hadron composites composed of 2 quarks selectable from the set ##[u, d, c, s, t, b, \bar u, \bar d, \bar c, \bar s, \bar t, \bar b]## satisfying the condition of having total charge = ##[-1, 0, 1]##. However, the superposition states of pure hadrons are sometimes also listed as new...
I recently watched this lecture "Quantum Fields: The Real Building Blocks of the Universe" by David Tong where the professor provides a succinct explanation of QFT in about 6 minutes around the midway mark.
The main point being that there are fields for particles and fields for forces and the...
This is from an examination paper -A level. My interest is on part (ii). Ok my take;
i. ##KE_{initial} = \dfrac {1}{2} mu^2= \dfrac {1}{2}× 0.4 ×12^2=28.8## Joules.
ii. ##\dfrac {1}{2} mv^2=\dfrac {1}{2} mu^2-mgh##
##0=28.8-(0.4×10×h)## where h is the vertical perpendiculor distance...
On page 160 in Shankar, he discusses how we get quantized energy levels of bound states - specifically for the particle in a box. We have three regions in space; region I from ## \ - \infty, -L/2 ##, region II from ## \ -L/2, L/2 ##, and region III from ## \ L/2, \infty ##. For the...
This is a very basic question, and I am not sure I have the answer.
A photon goes from point A to point B, only 1 meter distance apart from each other. A spacetime diagram would show a line connecting points A and B at a 45 degree angle. This can be a right triangle with equal sides, with...
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I am in 8th grade and 10 hours a day free time and i am highly motivated to learn some particle physics. What should i start with?
For part (a) and (b) of this problem,
The solution is,
However, how did they arrive at their conclusion in part(b)?
As you can't graph it on a GC, I decide to imagine plugging in values for t, which I see that the 2t^3 grows quicker than the t^2 which is why I think they said that the...
Hi,
unfortunately, I'm not that fit concerning the Lagrangian formalism, so I'm not sure if I solved the problem 1a correctly.
I have now proceeded as follows
the Lagrangian is
$$L=T-U$$
Since there are no constraining or other forces acting on the point mass, I assume that the...
I know how to construct Sy for spin = 1 case from the raising and lowering operators.
I get
$$
S_y=\frac{i\hbar}{\sqrt{2}}\begin{pmatrix}
0 & -1 & 0 \\ 1 & 0 & -1 \\ 0 & 1 & 0 \\
\end{pmatrix}
$$
From what I have seen, the eigenspinor for $\hbar$ is found by solving
$$...
I'm just starting to get into QFT as some self study. I've watched some lectures and videos, read some notes, and am trying to piece some things together.
Take ##U(1)_{EM}: L = \bar{\psi}[i\gamma^{\mu}(\partial_{\mu} - ieA_{\mu}) - m]\psi - 1/4 F_{\mu\nu}F^{\mu\nu}##
This allegedly governs spin...
i,j,k arevector
I know L=P*r=m*v*r=m(acosωti+bsinωtj)*(-aωsinωti+bωcosωtj)=mabw((cos^2)ωt+(sin^2)ωt)k=mabωk.
but why m(acosωti+bsinωtj)*(-aωsinωti+bωcosωtj)=mabw((cos^2)ωt+(sin^2)ωt)k.I need some detail.
please help me.
I just started my masters in "subatomic physics". The first year is the standard grad courses (electrodynamics, quantum and classical physics, statistical physics, maths etc.). The second year is going to be the one where I'll be choosing to become a theorist or experimentalist and write my...
When the expectation value of spin in the z direction for one particle is zero and I make measurements for an even number of particles in the same state, do I get exactly half to be spin up and half to be spin down along the z direction? More generally, what does spin expectation value for one...
Honestly, folks, I don't even know how to start. I included in the Relevant Equations section the relativistic generalization of the Larmor formula according to Jackson, because that's the equation for the power emitted by an accelerated particle, but I don't see how that gets me very far.
The...
If I want to get the spin angular momentum of a particle using the Stem-Gerlach experiment, I think I will find the spin 1/2 particle either spin up or spin down, but not both. I however want to ask this : Is there a non-zero probability that a particle which is spin-up in the z direction to be...
Dear readers,
I have a question regarding permanent magnets and the force they generate on particles, which is far from my comfort zone. I have the option on using two types of permanent magnets and with two different setups. Imagine that we want to attract small particles using the magnets...
Let us consider relativistic particle (electron) which moves with relativistic speed ##v## in the Coulomb field (in the field of a fixed heavy nucleus). The main question is what is the potential energy of a particle in such a static field? Landau and Lifshitz in their book "Field Theory"...
I was reading this interesting article [1] which talks about particle production in an expanding universe.
Usually this process is proposed to have occurred in the early universe, when the expansion was in the inflationary phase and it was so powerful that matter was created in particle...
Summary: The initial problem states: Consider a free particle of mass m moving in one space dimension with velocity v0. Its
starting point is at x = x0 = 0 at time t = t0 = 0 and its end point is at x = x1 = v0t1
at time t = t1 > 0. and this info is to do the 3 problems written out.
a)...
Hi, I have a question about the motion of a charged particle in crossed E and B fields. if B was pointing in the Z direction and E in the y direction then the component of the motion in the Z plane = 0. The only reason for this to happen is that the electric force due to the E field depends on...
I understand, and have unwillingly come to terms with the fact that virtual particles can carry negative momentum. This explains how momentum can be conserved in attractive forces via particle exchange.
I have a problem with this that I cannot reconcile...wouldn't this imply that as a particle...
The Lagrangian for a massless particle in a potential, using the ##(-,+,+,+)## metric signature, is
$$L = \frac{\dot{x}_\mu \dot{x}^\mu}{2e} - V,$$
where ##\dot{x}^\mu := \frac{dx^\mu}{d\lambda}## is the velocity, ##\lambda## is some worldline parameter, ##e## is the auxiliary einbein and...
Summary: Suppose that observer ##\mathcal{O}## sees a ##W## boson (spin-1 and ##m > 0##) with momentum ##\boldsymbol{p}## in the ##y##-direction and spin ##z##-component ##\sigma##. A second observer ##\mathcal{O'}## moves relative to the first with velocity ##\boldsymbol{v}## in the...
Hartle, Gravity
"An observer in an inertial frame can discover a parameter ##t##with
respect to which the positions of all free particles are changing at constant rates.
This is time"
Then goes on to say
"Indeed, inertial frames
could be defined as Cartesian reference frames for which Newton’s...
What is it the we detect in the first instance?
Is it the particle |wave or is it the field?
Is the former more fundamental than the latter in any sense or are we just talking the opposite sides of the same coin?
For instance does the em field create the photon and the electron or could...
The textbook I am self studying says that the wave function for a free particle with a known momentum, on the x axis, can be given as Asin(kx) and that the particle has an equal probability of being at any point along the x axis. I understand the square of the wave function to be the probability...
A question about the FLRW solution has confused a few of us. At time ##t_0## a particle has radial speed ##v_0^r## relative to the fundamental observers, and at a later time ##t_1## it has radial speed ##v_1^r##. The task is to show that\begin{align*}
\frac{a_0}{a_1} =\frac{v_1^r \gamma_1}{v_0^r...
d(ɣmv)/dt = qvB
(dɣ/dt)mv + ɣm(dv/dt) = qvB
Substituting gamma in and using the chain rule, it ends up simplifying to the following:
ɣ^3*m(dv/dt) = qvB
Now, I am confused on how to solve for v.
The following is the wave equation from Electrodynamics: $$\frac{\partial^2 \Psi}{\partial t^2} = c^2\frac{\partial^2 \Psi}{\partial x^2}$$ Where ##\Psi## is the wave function. But because of Heisenberg's Uncertainty, physicists had to come up with another equation (the Schrodinger equation)...
a) Find the energy levels of the ground state and the first excited state.
b) Find the wave functions (in the coordinate representation) of the ground state and the first excited state.
Hints: For a particle of mass m in a harmonic potential of angular frequency ω, the energy of the particle in...
What prevents making a particle accelerator better than the LHC but only a few centimeters big? After all, you accelerate objects with very small masses. Are there insuperable physical limits? What are the physical limitations?
if I have two particles in an entangled state, I make them travel in different directions, and I measure the state of only one of them then I know the outcome of the measurement of the other.
But when I take a measurement on the first particle, what happens to the second? Does it undergo a...
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A point charge of value q=8uC is released from rest at a point 1.5m away from the center of the axis of a ring with uniform charge density 3uC/m. The ring has a radius of 10 cm. What is the kinetic energy of this charge when it is 4.5 cm from the center of the charge ring, considering that it is...
My approach was: $$\psi_{2g} = \sqrt{1/L}sin(\frac{n \pi x}{2L}) = \sum c_n \sqrt {\frac{2}{L}} sin(\frac{n \pi x}{L})$$
Summarizing what i have done after that (Fourier series and sum of infinite series), we get the result realizing that, what we want matematically is ##P## $$P =...
The Hamiltonian of a particle of mass ##m## on the surface of a sphere of radius ##R## is ##H=\frac{L^2}{2mR^2}## where ##L## is the angular momentum operator. I want to solve the TISE ##\hat{H}\psi=E\psi## and in order to do that I rewrite ##L^2## in Schroedinger's representation in spherical...
My solution was as follows:
$$\frac {d\overrightarrow p} {dt}=q \frac {\overrightarrow v} {c}\times \overrightarrow B_0$$
The movement is in the ##[yz]## plane so ##|\overrightarrow v\times \overrightarrow B_0|=vB_0##, therefore: $$\biggr |\frac {dp} {dt}\biggr |= \frac {qvB_0} {c}.$$ On the...
I understand that the particle will be polarised according to its dielectric constant and the electric field across the capacitor.
However, since it is similar to an insulator and electrons do not move in and out of the particle easily, the particle will not be charged.
How then will...
(0:00 / 0:42) photon going light-speed blender simulation
I have no idea how a mathematician would translate this example into an equation. Every time I've worked with soft bodies I seem to run short of mathematicians buddies. Regardless of the mathematics of continuous object deformation, this...
The Schwarzschild metric implies a potential different from that of Newtonian gravity. Is there a relationship between it and the process by which particles can be absorbed by other particles?
(I haven't studied QFT yet)
I need to know if I have solved the following problem well:
A spin-less particle of mass m is confined to move on the surface of a cylinder of infinite height with a harmonic potential on the z-axis and Hamiltonian ##H=\frac{p_z^2}{2m}+\frac{L_z^2}{2mR^2}+\frac{1}{2}m\omega^2z^2## and I need to...
Can you tell the difference between two neutrons in an alpha particle? In one alpha particle, we know that the sum of the spins of two neutrons is zero. Can a neutron with upspin and a neutron with downspin be distinguished from each other? Or can't you tell because it's superimposed?
So I think I use the right approach and I get uncertainty like this:
And it's interval irrelevant(ofc),
So what kind of wave function gives us \h_bar / 2 ? I guess a normal curve? if so, why is normal curve could be? if not then what's kind of wave function can reach the lower bound
Suppose a molecule from our surrounding air (at ambient temperature) is being selected and is ionized. By some mechanical means, some velocity (say 100 m/s) is added to it and it has been put into a magnetic field perpendicular to its direction of motion. We all know how the molecule will behave...