Particle Definition and 1000 Threads

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...

Are there examples of particles with same size but different masses?

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...

How is it possible for a particle to be in two different states/places at the same instant?

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...

Free Kindle via Amazon, both part 1 and part 2 Part 1: https://www.amazon.com/dp/B00OD49Z96/?tag=pfamazon01-20 Part 2: https://www.amazon.com/dp/B00OD49Z00/?tag=pfamazon01-20 Enjoy

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...

Does a single charged particle in free fall into a black hole radiate?

(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...

In a quantum mechanical exercise, I found the following Hamiltonian: Consider a particle of spin 1 constrained to move on the surface of a sphere of radius R with Hamiltonian ##H=\frac{\omega}{\hbar}L^2##. I knew that the Hamiltonian of a particle bound to move on the surface of a sphere was...

The team has found that the particle, known as a W boson, is more massive than the theories predicted. The result has been described as "shocking" by Prof David Tobak, who is the project co-spokesperson. The discovery could lead to the development of a new, more complete theory of how the...

To solve a particle on a sphere problem in quantum mechanics we get the below equation :##\left[\frac{1}{\sin \theta} \frac{d}{d \theta}\left(\sin \theta \frac{d}{d \theta}\right)-\frac{m^{2}}{\sin ^{2} \theta}\right] \Theta(\theta)=-A \Theta(\theta) ## To solve this differential equation, we...

If experiments were conducted with a particle accelerator in a distant space from Earth or even our galaxy somewhere in the universe would the results change? I.e finding different elements ect..

Griffiths "introduction to elementary particles" serves a great introduction as a first course on particle physics for undergraduate students. But what are the possible alternatives of this textbook? Like being more beneficial in the long run, more time-consuming, for aspired students. But it...

"... two physical systems [seperated by wall], A1 and A2. A1 has ##\Omega_{1}(N1,V1,E1)## possible microstates, and the macrostate of A2 is ##\Omega_{2}(N2,V2,E2)## " "... at any time ##t##, the subsystem ##A_{1}## is equally likely to be in anyone of the ##\Omega_{1}\left(E_{1}\right)##...

Hello! I am trying to solve this exercise of the electric field, but it comes out changed sign and I don't know why. Statement: On a straight line of length ##L=60\, \textrm{cm}## a charge ##Q=3,0\, \mu \textrm{C}## is uniformly distributed. Calculate the force this linear distribution makes...

We know the net force on the charged particle in the uniform electric field pointing up is mg - qE. To get acceleration, divide the net force by mass to get g - qE/m Plug into kinematic equation and get velocity by itself and substitute$$\sqrt{h(2g - \frac{q \sigma}{\epsilon_o m})}$$

I can follow through all of this worked example until the final step 55/56x4.84= 4.75MeV Where does the 56 come from?

If ##\psi(x, t)=\left(\frac{1}{2 \pi \alpha^{2}}\right)^{1 / 4} \frac{1}{\sqrt{\gamma}} e^{i p_{0}\left(x-p_{0} t / 2 m\right) / \hbar} e^{-\left(x-p_{0} t / m\right)^{2} / 4 \alpha^{2} \gamma}##where * ##\gamma=1+\frac{i t} {\tau}##( a complex number) * ##\tau=\frac{m h}{2...

##W=-k(y\hat i+ x\hat j)d##. I am not getting the coordinate of particle correctly so that I can find the value of d. Also the force is varying.

I have been tasked with calculating amplitudes of a B meson decaying to a photon and lepton/lepton anti-neutrino pair ,upto one loop and have pretty much never seen this thing before. I will ask my questions along the way as I describe what I am doing. This factorization theorem seems to go thus...

Hi, I am doing my PHD in Nuclear/Particle Physics and I am getting all of the information I am using from papers, which are very specific. I feel like I am lacking general knowledge, which is likely to be tested in the defense. Do you know any book where I can get a better overview on Nuclear...

this is how i try to solve it: can someone please help me with that because i don't know what I am doing worng here.

Is the pole mass of the particle it's characteristic mass? When particle physicists calculate the mass of elementary particles, like top quark, do they mean the pole mass? If not what makes the apparent mass of a particle different from pole mass?

My answer so far in |S| = √3 /2 *hbar but the question states it must be an angular momentum. Is this an angular momentum or am I missing something? Thanks

The problem states to find the work per particle to assemble the following NaCl chain. I just want to post my work here to verify I have the correct answer. My work is attached in the image provided.

For the free particle in QM, the energy and momentum eigenstates are not physically realizable since they are not square integrable. So in that sense a particle cannot have a definite energy or momentum. What happens during measurement of say momentum or energy ? So we measure some...

Suppose there are two entangled particles A and B, separated by a few miles or light years. If the spin for particle A is observed, then from my understanding, A will experience quantum decoherence. And now we can be sure that B will have the opposite spin since B is entangled with A. Assuming...

I know that we can change the spin orientation of a spin 1/2 particle up or down and test it in the Stern Gerlach apparatus. And the spin 1/2 particles need two full rotations to return to the previous state. Questions: 1). what does state mean? 2). Is, Changing spin orientation to up or...

Summary:: What concentration for electrical engineering works on particle accelerators? What concentration for electrical engineering works on particle accelerators?

I've just started Quantum mechanics by McIntyre and have understood the following about operators which the author wrote till chapter 2: Each observable has an operator Operators act on kets to produce another kets. Only eigenvalues of an operator are possible values of a measurement. Now...

My attempt : ##\frac{\vec Ft^2}{2}=m\vec s## ##s=\frac{Ft^2}{2m}## ##P=\frac{W}{t}## ##k=\frac{\vec F\cdot \vec s}{t}## ##k=\frac{F^2t^2}{2mt}## ##k=\frac{F^2t}{2m}## ##F=\sqrt{\frac{2mk}{t}}## But there was an option which was ##2\sqrt{\frac{mk}{t}}##. And my assumption was that it was...

Aerosol particles with an average diameter of 5 μm and a density of 1000 kg / m3 are spread to a room with a floor area of 20 m2 and a height of 3.5 m. How long does it take for all 5 μm particles to settle on the floor (dry deposition)? The answer should be 1 hour and 20 minutes.

I have no idea where to even start with this, please help. I barely even know what integral of motion means.

not technically a homework question, just figured it fit here.

I calculated v=0 at t=3. s(3) =24 m. s(5)=16 m. So reverse distance that the particle travelled=24-16=8 m. So total distance =24+8=32 m.