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.
The final wave function solutions for a particle trapped in an infinite square well is written as:
$$\Psi(x,t) = \Sigma_{n=1}^{\infty} C_n\sqrt{\frac{2}{L_x}}sin(\frac{n\pi}{L_x}x)e^{-\frac{in^2{\pi}^2\hbar t}{2m{L_x}^2}}$$
The square of the coefficient ##C_n## i.e. ##{|C_n|}^2## is...
Hi I'm new to quantum mechanics, Looking for some help regarding a concept i am struggling to solve. I am curious if I had a cube of particles in a ground state and another cube with the same particle in a higher energy state.
If I placed one upon another, is there anything in quantum mechanics...
If I have a particle with a average lifetime of 15min, if I take 10 particles confined in a box, after 15 min there will be 5 particles.
After 15min 2.5 particles and so on... , but so, at the end there will be the last particle that decades.
That particle lived far longer than 15min, but is the...
If a charged particle moves through a potential difference, it gains kinetic energy but does it also lose potential energy?
When I accelerate a particle and then I "free it", what happen to its potential energy if the total energy should be conserved?
-1st: Could someone give me some insight on what a ket-state refers to when dealing with a field? To my understand it tells us the probability amplitude of having each excitation at any spacetime point, but I don't know if this is accurate. Also, we solve the free field equation not for this...
This is jut an example to illustrate my doubt. I don't know how to obtain the tracjectory given only the acceleration in this format. I realized that if i can show that there is an constat vector 'a' that satisfy a•r=constant, than the motion would be on the surface of a cone. So i tried to make...
Show that a point with acceleration given by:
a=c*((dr/dt)×r)/|r|3
where c is a constant, moves on the surface of a cone.
This is jut an example to illustrate my doubt. I don't know how to obtain the tracjectory given only the acceleration in this format. I realized that if i can show that...
Hi :) This is a problem from David Tong's Classical Dynamics course, found here: http://www.damtp.cam.ac.uk/user/tong/dynamics.html. In particular it is problem 6ii in the first problem sheet.
Firstly we can see the lagrangian is ##L = \frac{1}{2}m(\dot{r}^2+r^2\dot{\theta}^2+\dot{z}^2) -...
If ##\hat{T} = -\frac{\hbar}{2m}\frac{\mathrm{d^2} }{\mathrm{d} x^2}##, then the expectation value of the kinetic energy should be given as:
$$\begin{align*}
\left \langle T \right \rangle &= \int_{0}^{L} \sqrt{\frac{2}{L}} \sin{\left(\frac{\pi x}{L}\right)}...
I tried solving the problem using the force formula, so what I have known is the magnetic field B and E. I also have a motion in the x-axis, that means that the velocity will be pointed at the x-axis. Inserting this in the formula I will be having something like this:
$$\mathbf{F} = q(\mathbf{E}...
Consider that the particle is moving in circular with tangential velocity v, and (0,0)is its origin.
I wonder why dr/dt is equal to tangential velocity instead of radial velocity (since dr/dt means how much change in radial distance in a really short duration of time)
I am doing a learning project by writing a simulation that includes capacitance and current flow amongst capacitors that may potentially be in parallel. I don't care about certain details yet - dissipation factor, frequency dependent effects, temperature. Tiny capacitences within diode junctions...
I have been reading about ontologies in quantum physics recently and I came across Bohmian mechanics. If I understood it correctly BM endorses Particle ontology. Particle ontology claims that point-like particles that move continuously in time are the fundamental building blocks.
I know some...
So I think I have the principles mixed up here because I'm getting kind of "circular" answers.
## N = N_1 + N_2##
##dN## = 0 bc/ particle number fixed so ##dN_1 = -dN_2##
##F = cN^2 = c(N_1 + N_2)^2##
In diffusive equilibrium, free energy would be minimized and chemical potentials equal...
$$...
I am starting my Master's Degree in Nuclear and Particle Physics, should i invest in taking a course in Parallel Computation? I know the role that Parallel Computation has in particle physics, but is there any use in a particle physicst learning about parallel computation, or could it be...
Hi, my son is fan of the Quantum Physics and we developed a cloud chamber. I'm attaching an image of particle sequence and I will like to find some help to know witch particle is. I will appreciate any help on it. Thanks
How does the photoelectric effect prove the wave-particle wrong? Higher intensity does not mean higher energy. If we were to assume the wave-particle model, an increase in intensity means an increase in the amplitude of the wave right? The energy of light is never dependent on amplitude, it is...
I have attempted a solution using conservation of momentum. Could people help check if this solution is correct (the result looks weird), as the problem doesn't have solution with it.
$$
\begin{aligned}
\begin{pmatrix}Mc \\ 0\end{pmatrix} &= \begin{pmatrix}E_R/c \\ \mathbf{p}_R\end{pmatrix} +...
General relativity tells us that an object in free-fall is actually inertial, following a geodesic through curved spacetime, and not accelerating. Instead, it's objects like us, on the surface of a large body, that are accelerating upwards.
Maxwell's equations also tell us that accelerated...
I imagine a particle traveling across 1 wave cycle. The total vertical distance traveled across the wave cycle is 4 x the amplitude of the wave. The total vertical distance traveled in 1 minute:
5 cycles in 1 second, thus 5x60 cycles in a minute
then 4 x amplitudes effectively traveled per...
I would like to estimate the maximum acceleration (or deceleration) of an alpha particle that is backscattered by a heavy atom, like in Rutherford backscattering. I am interested in the order of magnitude, not in a precise value. I am assuming the collision is elastic.
The kinetic energy of the...
I was reading this article at Wikipedia that says particle physics predicts that the cosmological constant is 10^120 larger than per observation:
https://en.wikipedia.org/wiki/Anthropic_principle
I came across this 'problem' when I was trying to think about how a torsion spring would apply torque in something like a miniature catapult.
I understand that in the context of something like turning a wrench, we can find the net torque on the wrench by treating the hand applying the force as...
Hello,
I have a particle at point A with charge ##q_A##, and an unmovable sphere of radius ##R_B## at point B with a volumic charge density ##\rho##. The distance from particle A to the centre of the sphere in B is ##r##. Both objects have opposed charges, so, the particle in A, initially at...
Since it asks for the time evolution of the wavefunction in the momentum space, I write : ##\tilde{\Psi}(k,t) = < p|U(t,t_{0})|\Psi> = < U^\dagger(t,t_{0})p|\Psi>##
Since ##U(t,t_{0})^\dagger = e^{\frac{i}{\hbar}\frac{\hat{p^2}t}{2m}}##, the above equation becomes
##\tilde{\Psi}(k,t) =...
For a massless particle let\begin{align*}
S[x,e] = \dfrac{1}{2} \int d\lambda e^{-1} \dot{x}^{\mu} \dot{x}^{\nu} g_{\mu \nu}(x)
\end{align*}Let ##\xi## be a conformal Killing vector of ##ds^2##, then under a transformation ##x^{\mu} \rightarrow x^{\mu} + \alpha \xi^{\mu}## and ##e \rightarrow e...
I am interested on how Feynman diagram is formed from a differential equation model of particle interaction wherein the incoming particles are not bound (e.g., separated neutron, proton and electron) and one or more of the outgoing particles are bound (e.g., hydrogen atom). However, I had never...
Knowing that ##F(x)=-\mathrm{d}V(x)/\mathrm{d}x##, I found that ##F(x)=-2.4x^3+1.35x^2+8x-3##. But it was the only thing I could find. How can I analyze what will be the type of movement with the information presented by the question statement?
According to Wikipedia,
The particle horizon is the maximum distance from which light from particles could have traveled to the observer in the age of the universe. It represents the boundary between the observable and the unobservable regions of the universe, so its distance at the present...
Which experimental physics branch has better job prospects (both inside and outside academia) - particle physics or nuclear physics? Is the difference very big?
Say we just created a particle (high probability of one-particle state), is the probability of a very far away detector getting triggered at the time of creation (probability of finding a particle outside of its light cone) zero according to QFT?
Since we can detect particles and make...
The question is below. I tried reasoning that because x is constant, E is also constant however that gives me values in the range of 10^51. Then I tried to use numpy's ivp_solve function to solve the differential equation however I wasn't able to get that working either. Apparently I'm meant to...
At t= 0, we can see that the particle P has a radial acceleration of ##-2\hat j## and a tangential acceleration of ##2 \hat i##. The radial acceleration will tend to move it in a circle of a certain radius, whereas the tangential acceleration will tend to displace it parallel to x- axis...
I find a exercise in Leonard Susskind's book Classical Mechanics
the Hamiltonian of a charged particle in a magnetic field(ignore the electric field) is $$H=\sum_{i} \left\{ \frac{1}{2m} \left[ p_{i}-\frac{e}{c}A_{i}(x) \right]\left[ p_{i}-\frac{e}{c}A_{i}(x) \right]...
Hello! In most of the modern mass measurements in a penning trap, they cool down the degrees of freedom of the ion (the 3 eigenmotions) using resistive cooling, in which they couple an external circuit to some of the electrodes of the trap and the ion is cooled down to the temperature of the...
This question is very confusing since I don't see two distinct particles that are exerting a gravitational force on each other. Also to complicate matters, a gas is made of many individual particles and I don't know how to determine the gravitational force on a single particle from so many other...
Consider the system of the mass and uniform disc.
Since no external forces act on the system, the angular momentum will be conserved. For elastic collision, the kinetic energy of the system stays constant.Measuring angular momentum from the hinge:
##\vec L_i = Rmv_0 \space\hat i + I \omega_0...
Curious about this (https://en.wikipedia.org/wiki/Particle_accelerator)
which indicates diminishing returns on new particle accelerators. However to uncover new physics, presumably you need to keep increasing the Lorentz factor by the roughly 10x trend here:
So is this hopeless?
I have read that if the exchangeparticle of an interaction has even spin then the force between them is
attractive if the charge is equal (gravitation) and repulsive if the charge is not equal.
Is this wright?
Two forces each of size 8N, have a resultant of 13N.
a) Find the angle between the forces
b) The two given forces of magnitude 8N act on a particle of mass m kg, which remains at rest on a horizontal surface with no friction. The normal contact force between the surface and the particle has...
I tried to resolve this problem with youtube tutorials help, but, i have a many wrong results. The teacher says that the problem requires critics points, so i know that for that points i need a second grade ecuation, but i don't know how interpreter that points. My results: PD: I don't know how...
I think I made an error somewhere. In ##[0,a]## I let ##\varphi(x) = \varphi_1(x) := p\sin{kx}## whilst in ##(\xi, \infty)## I let ##\varphi(x) = \varphi_2 (x) := re^{-\gamma x}##, and the constraints at ##x=\xi## are \begin{align*}
\varphi_1'(\xi) = \varphi_2'(\xi) &\implies pk\cos{k\xi} =...
I was going to put this in the homework forums, but on second thoughts it's more conceptual so perhaps here is better. It's about problem 4, chapter 6 of Wald. Part (a) is fine, $$u^a \nabla_a u^b = \frac{\xi^a}{(-\xi^c \xi_c)^{1/2}} \left( \frac{\nabla_a \xi^b}{(-\xi^c \xi_c)^{1/2}} +...
A table with smooth horizontal surface is fixed in a cabin that rotates with a uniform angular velocity ω in a circular path of radius R. A smooth horizontal groove AB of length L(<<R) is made on the surface of the table. The groove makes an angle θ with the radius OA of the circle in which the...
Hello!
I am taking a course on Electroweak & Strong Interactions (you could equally call it Standard Model I) and I find it absolutely fascinating! 😍
We studied how weak interactions violate parity, introduction to QCD, flavor physics (CKM matrix, CP violation, …) and neutrino physics...
Hi all
Another random, kinda open-ended question here. Sorry for that. I found myself reading about atomizing nozzles in oil burners, and got curious about the physics of atomized sprays. I didn't have much luck researching this on my own, so I'm turning to you all. It was the kind of situation...