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4
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2answers
155 views

Vector potential

I have difficulty understanding the following vector calculus example. Text can be found here. It is the 5th Q&A -- starting with equation (31.1035).It concerns finding the vector potential of a ...
3
votes
2answers
436 views

Coherent State, Unitary Operators, Harmonic Oscillator

Consider the operator: $$O = e^{\theta(a^\dagger b - b^\dagger a)}$$ where $\theta$ is a constant. $O$ is a unitary operator. $a$, $a^\dagger$, $b$, and $b^\dagger$ are ladder operators for two ...
1
vote
1answer
325 views

Eigenfunctions in a harmonic oscillator

This assignment is about the one dimensional harmonic oscillator (HO). The hamiltonian is just as you know from the HO, same goes for the energies, but I get that the wavefunction of the particle, at ...
-2
votes
4answers
838 views

Resistors in Parallel

From my book: "A length of wire is cut into five equal pieces. The five pieces are then connected in parallel, with the resulting resistance being 2.00 Ω. What was the resistance of the ...
1
vote
2answers
456 views

How can I solve for time without knowing the vertical velocity?

A guy posted this problem on a forum: There is a bird sitting on a pole of height h. you throw a rock at it and the moment the rock leaves your hand the bird starts flying horizontally away from ...
-1
votes
1answer
110 views

Lifting house with balloons [closed]

I have an assignment about the movie Up. Here is the question: Critique the brief floating scene. Did the animators use enough balloons during this scene? What important variables, (which affect ...
3
votes
1answer
621 views

Pendulum in an elevator

Suppose we have a pendulum tied to the ceiling of an elevator which is at rest. The pendulum is oscillating with a time period $T$, and it has an angular amplitude, say $\beta$. Now at some time ...
1
vote
1answer
339 views

Apparent and real depth object in water [closed]

Did I get my formula right? Seems like the correct answer is $d_o = 1.33 \times d_i$ but I thought the formula I should use is $d_i = - \frac{n_2}{n_1} d_o$
2
votes
1answer
415 views

Time evolution operator to find expectation value

I have a state $\Psi (x,0) = \sum_{n=0}^{\infty} c_{n}u_n(x)$ and want to find the expectation value of any observable A at time t, $\langle \Psi(t)|\hat{A}|\Psi(t)\rangle$. I know that I should ...
1
vote
4answers
2k views

Capacitor Charging and Discharging when connected to the ground

When we charge a capacitor using a battery and then remove the battery, the plates of capacitor becomes charged. One holds positive charge and the other one gets equal negative charge. o. k. ? Now ...
2
votes
1answer
163 views

Liquid benzene magnetic susceptibility

In a solid state physics problem, I'm asked to make a rough estimate of the contribution to the diamagnetic susceptibility of the outer electron of each carbon atom. The wavefunction of these ...
4
votes
2answers
354 views

Proof for commutator relation $[\hat{H},\hat{a}] = - \hbar \omega \hat{a}$

I know how to derive below equations found on wikipedia and have done it myselt too: \begin{align} \hat{H} &= \hbar \omega \left(\hat{a}^\dagger\hat{a} + \frac{1}{2}\right)\\ \hat{H} &= ...
4
votes
2answers
100 views

What's the physical difference between the quantities $\langle v_{i}v_{j}\rangle$ and $\langle v_{i}\rangle\langle v_{j}\rangle$?

What's the physical difference between the quantities $\left\langle v_{i}v_{j}\right\rangle $ and $\left\langle v_{i}\right\rangle \left\langle v_{j}\right\rangle $? Where $\left\langle ...
2
votes
3answers
371 views

How to determine the direction of medium's displacement vectors of a standing wave?

Consider the following problem taken from a problem booklet. My questions are: What is displacement vector? And how to determine the direction of displacement vector at a certain point? Where is the ...
1
vote
2answers
213 views

Calculating the change in entropy in a melting process

I have a homework question that I'm completely stumped on and need help solving it. I have a $50\, \mathrm{g}$ ice cube at $-15\, \mathrm{C}$ that is in a container of $200\, \mathrm{g}$ of water at ...
0
votes
1answer
151 views

Reachable area of cannonball given fixed initial speed [closed]

The trajectory of a cannonball fired from the origin with initial speed $v_0$ at an angle $\theta$ is given by $$y = x\tan\theta - \frac{g}{2v_0^2 \cos^2\theta}x^2.$$ For fixed $v_0$, at what angle ...
0
votes
1answer
431 views

Spacetime and Timelike Intervals

The difference between a “timelike” spacetime interval and a “spacelike” spacetime interval can be understood in the following way: If the spacetime interval between two events is timelike, there ...
2
votes
1answer
197 views

Induced Current, Dipole Falling Under Gravity Towards Circular Loop [closed]

Suppose a magnetic dipole $\mathbf{m} = m \hat{z}$ is falling towards a circular loop of radius $b$ under gravity. Assuming the dipole always stays along the $z$-axis of the loop, determine the ...
2
votes
2answers
456 views

Hamiltonian of Harmonic Oscillator with Spin Term

We have the usual Hamiltonian for the 1D Harmonic Oscillator: $\hat{H_{0}}=\frac{\hat{P^2}}{2m} + \frac{1}{2}m \omega \hat{X^2}$ Now a new term has been added to the Hamiltonian, $\hat{H} = ...
0
votes
2answers
142 views

Escape velocity to intersection of two gravitational fields

Find the minimal velocity needed for a meteorite of mass $m$ to get to earth from the moon. Hint: the distance between the center of earth and the center of moon is $\approx 60 R_E$, and the ...
2
votes
1answer
133 views

Physical significance of effective wave function

In Yanhua Shih's book on quantum optics, the coherence functions are expressed in terms of effective wave function. Here are the expressions for single photon wave packets. To derive the coherence ...
1
vote
2answers
129 views

The electric potential and the electric field

I'm preparing for my school exam in physics and I found that I don't understand the derivation of $E = -\nablaφ$. Here is a derivation from my book: 1) Imagine that 1 and 2 are infinitely close ...
0
votes
1answer
1k views

Calculating the coefficient of thermal expansion in liquid

I am trying to write a matlab function that calculates the coefficient of thermal expansion of water from a given temperature. From what I understand the thermal expansion coefficient is calculated as ...
2
votes
1answer
452 views

How we approach RLC circult from RLGC model?

In the text, it introduces a practical model to investigate a transmission line (like BNC cable), it considers the transmission line has resistive $R$, inductance $L$, conductance $G$ and capacitance ...
-4
votes
1answer
2k views

man walking in rain:relative velocity [closed]

A man walking in rain at a speed of 3kmph find rain to be falling vertically. When he increases his speed to 6 kmph, he finds rain meeting him at an angle of 45 deg to the vertical. What is the ...
1
vote
3answers
396 views

Man in elevator, holding it, on a scale

This is the scenario where my mass is $60 kg$, the mass of the elevator is $30kg$, and due to a malfunction, I have to hold myself and the elevator at rest. The question is, if there is a weighing ...
3
votes
2answers
194 views

Probability of position in linear shm?

The problem that got me thinking goes like this:- Find $dp/dx$ where $p$ is the probability of finding a body at a random instant of time undergoing linear shm according to $x=a\sin(\omega t)$. ...
2
votes
1answer
75 views

Gas Laws And Adiabatic Process

Air at 20 degrees Celsius is compressed adiabatically from 1 bar to 10 bar, what will its temperature be? With $$P_1 = 1,$$ $$P_2 = 10$$ $$T_1 = 293K,$$ $$T_2 = unknown$$ using ...
2
votes
1answer
328 views

What defines the adiabatic flame temperature?

What defines the adiabatic flame temperature? In a case I have to solve, I need to describe the combustion of natural gas (Groningen natural gas, to be specific). However, I am having some problems ...
-4
votes
1answer
91 views

High School Physics student needs help [closed]

A human cannon has a spring constant of 35 000 N/m. The spring can be extended up to 4.5m. How far horizontally would a 65kg clown be fired if the cannon is pointed upward at 45 degrees to the ...
0
votes
0answers
172 views

Determining the length of a Torsional Pendulum

Currently working on this question, however I'm not sure how to solve it. As a pendulum swings in simple harmonic motion at the surface of the Earth, the angle the pendulum makes relative to its ...
4
votes
1answer
344 views

Conservation of momentum in collision of two bodies

Suppose we have some ramp on wheels of mass $M$, standing on a frictionless surface. A cart of mass $m$ moves with a certain velocity $v$ towards the ramp. The cart moves up the ramp ...
0
votes
2answers
1k views

Stopping distance of two objects with equal Kinetic Energy

I'm working on a problem regarding two objects with the same kinetic energy. Two objects with masses of $m_1$ and $m_2$ have the same kinetic energy are both moving to the right. The same constant ...
1
vote
3answers
186 views

Error calculation with linear regression

I am trying to determine the boltzmann constant by using a bipolar junction transistor. In my circuit (apparently I don't have enough point to join a image sorry), the Ebers and Moll model gives the ...
0
votes
1answer
209 views

Time Dependent HydroHow would I go about writing the time dependent wave function given the wavefunction at $t=0$? gen Wave Function

1) How vwoulHow would I go about writing the time dependent wave function given the wavefunction at $t=0$? go about writing the time dependent wave function given the wavefunction at $t=0$? ...
2
votes
2answers
366 views

Ricci tensor for a 3-sphere without Math packets

Let's have the metric for a 3-sphere: $$ dl^{2} = R^{2}\left(d\psi ^{2} + sin^{2}(\psi )(d \theta ^{2} + sin^{2}(\theta ) d \varphi^{2})\right). $$ I tried to calculate Riemann or Ricci tensor's ...
0
votes
3answers
73 views

Interaction photons-matter and dimensional analysis

I know that when photons pass through matter, the law that describes the intensity in function of the thickness is: $$I(x)=I_0 e^{-\mu x}$$ where $\mu = \rho \frac{N_a}{A} \sigma$ and ...
-1
votes
1answer
69 views

Charge gained due to photoelectric effect [closed]

Here I think, one beam will knock out just one electron. So, I am not able to even understand what the question says. Please someone give a hint as to what the question asks... As source of the ...
3
votes
1answer
157 views

Tension of rope in the gravitational field of earth

Two balls of mass $m$ each one are connected with mass-less rope with the same length as the radius of earth. The system is in free fall. Prove that the tension of the rope when the nearest (to ...
-1
votes
1answer
239 views

Acceleration, velocity and speed

It is given that acceleration is constant, so can we infer that average speed and velocity are the same?? Moreover, circular motion is out of the question, as the function of x(t) where ...
1
vote
1answer
176 views

Volume of gas at which relative fluctuation of gas density occurs

I have the following question: In what volume of gas occurs 10 % relative fluctuation of gas density under pressure of $10^5\text{ Pa}$ and temperature of $293.15\text{ K}$? I don't understand ...
0
votes
1answer
343 views

Damped oscilator - logarithmic decrement of damping

Could you please tell me, where is the mistake? What is the logarithmic decrement of damping $Λ$ of damped harmonic oscillator, if its mechanical energy decreases to the 50% of its initial value ...
1
vote
0answers
498 views

How to calculate Riemann and Ricci tensors for a sphere? [closed]

Let's have the metric for a sphere: $$ dl^{2} = R^{2}\left(d\psi ^{2} + sin^{2}(\psi )(d \theta ^{2} + sin^{2}(\theta ) d \varphi^{2})\right). $$ I tried to calculate Riemann or Ricci tensor's ...
0
votes
1answer
175 views

A Type of Pendulum [closed]

Is there any chance that $$rtl(\ddot\omega+\ddot\phi)\cdot\sin{(\phi+\omega t)}- gl\dot\phi \cdot \sin{\phi} + ltr\dot\omega(\dot\phi^2-\dot\omega)\cdot \cos{(\phi+\omega t)}-gtr\cos{(\omega ...
0
votes
0answers
79 views

What does this notation mean in terms of quantic numbers, and how to imagine the electrons in this quantic system? (Helium $2^1$ $P$ and $2^3$ $P$)

Helium atom in the $2^1$ $P$ and $2^3$ $P$ excited states Now I'm guessing that 1 electron should be considered in the 1s state, but what about the other? Should I consider the other as simply ...
0
votes
1answer
333 views

Contraction of the metric tensor

This is perhaps a simple tensor calculus problem -- but I just can't see why... I have notes (in GR) that contains a proof of the statement In space of constant sectional curvature, $K$ is ...
1
vote
1answer
2k views

Projectile along incline [closed]

A particle is projected with velocity $u$ from the bottom of an inclined plane whose inclination with the horizontal is $\beta$. If afterwards the projectile strikes the inclined plane perpendicular ...
1
vote
2answers
996 views

The potential and the intensity of the gravitational field in the axis of a circular plate

Calculate the potential and the intensity of the gravitational field at a distance $x> 0$ in the axis of thin homogeneous circular plate of radius $a$ and mass $M$. Could anybody describe how to ...
2
votes
1answer
73 views

Finding the coffecient of restitution

A ball moving with velocity $1 \hat i \ ms^{-1}$ and collides with a friction less wall, afetr collision the velocity of ball becomes $1/2 \hat j \ ms^{-1}$. Find the coefficient of restitution ...
3
votes
1answer
409 views

Schrödinger equation for a harmonic oscillator

I have came across this equation for quantum harmonic oscillator $$ W \psi = - \frac{\hbar^2}{2m}\frac{d^2\psi}{dx^2} + \frac{1}{2} m \omega^2 x^2 \psi $$ which is often remodelled by defining a new ...