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2
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2answers
646 views

Plotting $\psi$ for finite square well potential

Lets say we have a finite square potential well like below: This well has a $\psi$ which we can combine with $\psi_I$, $\psi_{II}$ and $\psi_{III}$. I have been playing around and got expressions ...
2
votes
1answer
136 views

Varying an action (cosmological perturbation theory)

I am stuck varying an action, trying to get an equation of motion. (Going from eq. 91 to eq. 92 in the image.) This is the action $$S~=~\int d^{4}x \frac{a^{2}(t)}{2}(\dot{h}^{2}-(\nabla h)^2).$$ ...
2
votes
2answers
5k views

Equations for an object moving linearly but with air resistance taken into account?

I know (from Kinematics) that for an object moving linearly with an acceleration and without air resistance the following equations can be used to determine v(velocity) or x(position of the object) at ...
1
vote
2answers
106 views

Kinematics question - Newton's Law of Motion [closed]

Question: Find the mass M of the hanging block in the following figure which will prevent the smaller block from slipping over the triangular block. All the surfaces are frictionless and the strings ...
1
vote
1answer
72 views

How much wind does it take to tip a sign over? [closed]

Or said another way - how much counterweight does the base of a sign need to keep it from tipping over given a specific max wind? Assume the sign does not let wind through Assume the base of the ...
1
vote
2answers
113 views

A question about canonical momentum and arbitrariness for potential in magnetism

The following question confuses me: There exists magnetic field $B_z =- \beta x$ where $x > 0$, and a particle is incident from origin point $(0,0)$ with pisitive charge $q$, mass $m$, and ...
1
vote
1answer
180 views

Motion of block on wedge

there is some confusion to me in the case of "motion of block on a frictionless wedge" Below is a simple diagram! Let us consider a situation as above in which there is a block of mass $m$ moving ...
1
vote
1answer
215 views

Finding the Basis vectors of a Killing field vector space

I have solved the Killing vector equations for a 2-sphere and got the following answer. $A,B,C$ are three integration constants as expected. $$\xi_{\theta}=A \sin{\phi}+B\cos{\phi}$$ ...
1
vote
1answer
77 views

How large of a solar sail would be needed to travel to mars in under a year?

I'm attempting to approach this using the identity $$F/A = I/c$$ I can solve for Area easily enough $$A = F(c/I)$$ and I know the distance $d$ is $$d=1/2(at^2)$$ But I'm having difficulty trying to ...
1
vote
0answers
125 views

Use of Principle of Equivalence

Let $x^\mu$ be the coordinates of a reference frame, $K$, where all bodies feel the same constant and uniform acceleration $\textbf{a}=\textbf{g}=-\nabla\varphi$; let $\xi^\mu$ be the coordinates of a ...
1
vote
1answer
326 views

Two Qubit problem

A two-qubit system was originally in the state $ \frac{3}{4}|00\rangle-\frac{\sqrt{5}}{4}|01\rangle+\frac{1}{4}|10\rangle-\frac{1}{4}|11\rangle $ , and then we measured the first qubit to ...
1
vote
1answer
557 views

Force exerted on potential wall

A particle bound in an infinite potential wall at $x=0$ will apply a force on the wall. For a plane wave and imagining it as a fluid bouncing off the reflection wall at $x=0$, find the force in terms ...
1
vote
2answers
368 views

Motion of a rod struck at one end

Imagine a strong metal rod of uniform density and thickness floating in a weightless environment. Imagine it lies on an X-Y plane, with one end (A) lying at 0,0, and the other end (B) at 0,1. Then it ...
1
vote
1answer
1k views

Calculation for force generated by a rotating rectangular blade

When trying to calculate the lift force generated by a simple rectangular blade, I've found the following equation: $$F = \omega^2 L^2 l\rho\sin^2\phi$$ in which $\omega$ is the angular velocity, $L$ ...
1
vote
1answer
240 views

Knowing the mass and force acting on a particle, how do we derive the relativistic function for velocity with respect to time?

Use this scenario: An electron gains speed in the Stanford Linear Accelerator (SLA) across 3000 meters, reaching a final velocity of 0.95c due to a constant force pushing on the electron. Given the ...
0
votes
1answer
180 views

Free body diagram of rod in sphere

I was finding the free body diagram part of dynamics quite easy until I found this question , Here's how it goes : A rod AB is placed inside a spherical shell, whose inside surface is rough. Draw ...
0
votes
1answer
401 views

Rigid bar suspended by two ropes, tension of first rope after second rope is cut?

This is from a practice exam, I've been sitting here thinking about it for over an hour and can't convince myself of an answer, or write down any relevant exact equations. A bar of uniform density ...
-1
votes
1answer
274 views

Speed of a falling pencil [closed]

If you balance a pencil of length $d$ on its tip, and let it fall, how do you compute the final velocity of its other end just before it touches the ground? (Assume the pencil is a uniform one ...
-2
votes
2answers
3k views

Newton Laws of Motion + Effective spring Constant [closed]

! Can someone please help me in solving this question: What is the effective spring constant for the system of the two springs, perfect pulley, and string shown on the left for it to be modeled ...
8
votes
5answers
524 views

How to get the position operator in the momentum representation from knowing the momentum operator in the position representation?

I know that $$\tag{1}\hat{p}~=~-i\hbar \frac{\partial}{\partial x}~.$$ How can I get $$\tag{2}\hat{x}~=~i\hbar \frac{\partial}{\partial p}~?$$ I think this simple and I'm just over thinking it, ...
6
votes
1answer
567 views

Lorentz Invariant Integration Measure [closed]

When we canonically quantize the scalar field in QFT, we use a Lorentz invariant integration measure given by $$\widetilde{dk} \equiv \frac{d^3k}{(2\pi)^3 2\omega(\textbf{k})}.$$ How can I show that ...
5
votes
1answer
313 views

Do mutual eigenkets imply commutation of two operators?

I have been working on this question. I have solved it, and I would like to check whether my line of reasoning is right or wrong Question: Prove that if there exists a mutual complete set of ...
5
votes
1answer
260 views

Divergence theorem in complex coordinates

This question is related to Stokes' theorem in complex coordinates (CFT) but, I still don't understand :( Namely how to prove the divergence theorem in complex coordinate in Eq (2.1.9) in ...
5
votes
3answers
836 views

Why do we take small steps while walking on ice?

When we walk on ice we should take small steps. Small steps ensure: a.)larger friction. b.)small friction. c.)larger normal force. d.)smaller normal force. The correct ...
5
votes
2answers
149 views

Generalizing a relativistic kinematics formula for spatial-acceleration dependence

I'm starting from this expression $$ \alpha dt = \gamma^3 dv $$ where $\alpha$ is proper acceleration of a point particle, $dv$ and $dt$ are coordinate differentials of velocity and time, and ...
4
votes
3answers
148 views

Using 2D position, velocity, and mass to determine the parametric position equations for an orbiting body

I have a gravity-related question. I am programming an orbit simulator. I have everything up and running, but I would like to render the smaller body's orbital path (the larger body is fixed). To do ...
4
votes
0answers
177 views

Hamiltonian function for classical hard-sphere elastic collision

I'm trying to find the Hamiltonian function for a system consisting of a single particle in one dimension colliding elastically with a wall at x = 0. Everything I've read on the topic (e.g. this ...
4
votes
1answer
677 views

Electric Field from Dielectric Shell

This is a question taken from a past E&M exam A thick spherical shell (inner radius $R_1$ and outer radius $R_2$) is made of a dielectric material with a "frozen in" polarization ...
4
votes
1answer
101 views

Photon Escape Angle From Black Hole

Consider a photon source emitting photons near the surface of a Schwarzschild black hole. What angle, as a function of the source's radius from the event horizon, must the photons be emitted at such ...
3
votes
0answers
183 views

Wald problem 4 of chapter 4

I'm trying to derive equation 4.4.51 in Wald's GR book (the second order correction in $\gamma$ term for the Ricci tensor): where $g=\eta+\gamma$. So ...
3
votes
1answer
207 views

Fermi-Dirac distribution derivation?

I am trying to derive the Fermi-Dirac statistics using density matrix formalism. I know that $$<A>= Tr \rho A.$$ So I started from $$<n(\epsilon_i)>= Tr \rho n(\epsilon_i)=\frac {1}{Z} ...
3
votes
2answers
144 views

Proper Time with a non-zero Initial Velocity

I have a question regarding how to find the proper time for a body with an initial velocity to slow down to 0. For example, the equation I have been working with looks like: $$\int^\tau_0 ...
3
votes
2answers
378 views

Geodesic equations

I am having trouble understanding how the following statement (taken from some old notes) is true: For a 2 dimensional space such that $$ds^2=\frac{1}{u^2}(-du^2+dv^2)$$ the timelike geodesics ...
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 ...
3
votes
2answers
2k views

block slides on smooth triangular wedge kept on smooth floor.Find velocity of wedge when block reaches bottom

Find the velocity of the triangular block when the small block reaches the bottom: Here is what I did: The final velocity(at the bottom)of the small block of mass m is $\sqrt{2gh}$ along the plane ...
3
votes
1answer
334 views

Lab observation correct? As distance decreases, velocity increases, stderr decreases

The experiment goes like this: Allow a moving cart to move from the top of an incline plane ($x_0$) downwards. The time taken will be recorded by the picket fence (those things you see wired up). ...
3
votes
2answers
1k views

First integral of an equation of motion: $\mu\ddot r=-\frac{k}{r^2}$

I've got an equation of motion (EOM), which is $ \mu\ddot r=-\frac{k}{r^2} $ How do I find the first integral of this EOM? I'd appreciate it if someone could show me the steps involved. I should ...
3
votes
2answers
143 views

Derivatives of delta function and equation of continuity for a single charge…

For a single charge $e$ with position vector $\textbf R$, the charge density $\rho$ and and current density $\textbf{j}$ are fiven by: \begin{equation} \rho(\textbf{r},t)= ...
3
votes
3answers
400 views

Braking distances on a rainy road

I am curious to find the braking distance for a car on a road. In attempting to find this out, I found that the braking distance for a car (on a flat road) is $$ d = \frac{v^2}{2\mu g} $$ where ...
3
votes
2answers
967 views

What potential energy functions are mostly used in Schrodinger equation?

In the time-independent Schrodinger equation $$\left(-\frac{\hbar^2}{2m}\Delta+V(\mathbf{r})\right)\psi(\mathbf{r})=E\psi(\mathbf{r})$$ What functions $V(\mathbf{r})$ are mostly used in research ...
3
votes
2answers
2k views

Simple harmonic motion problem

Problem: An object is undergoing simple harmonic motion with period 1.2s and amplitude 0.6m. At $t=0$, the object is at $x=0$. How far is the object from the equilibrium position when $t=0.480$s? ...
2
votes
3answers
66 views

Elastic collision of point particle and rod

A 1 meter long rod on the ice with mass $m_2=1$ kg is perpendicularly hit on one end by a point particle with mass $m_1=0.1$ kg. The collision is elastic and the point particle is bounced back in ...
2
votes
1answer
58 views

Relation between electric potential and wavelength of an electron

"An electron that is accelerated from rest through an electric potential difference of $V$ has a de Broglie wavelength of $\lambda$. Investigate the relationship between $V$ and $\lambda$." I had two ...
2
votes
1answer
120 views

RMS Free Path vs Mean Free Path

I am trying to determine the mathematical difference between mean free path and root-mean-square free path. For an ideal gas, the relaxation time is $$\tau=\frac{1}{\sqrt2 \pi nd^2 \bar v}$$ and the ...
2
votes
0answers
208 views

Equation of motion for a falling rod (with one end touching a frictionless surface)

I have a quick question about the equation of motion for a falling rod (with one end touching a frictionless surface). The end touching the surface is not fixed. I am given the moment of inertia about ...
2
votes
2answers
219 views

Wave function of a particle in a gravitational field

Suppose we have a particle with mass $m$ and energy $E$ in a gravitational field $V(z)=-mgz$. How can I find the wave function $\psi(z)$? It should have an integral form on $dp$. Any help would ...
2
votes
2answers
1k views

How To Use Ladder Operators?

I'm studying for a test in quantum mechanics and I'm having a hard time understanding how to use ladder operators. There are no examples in my text book, only definitions that I can't understand how ...
2
votes
0answers
219 views

Loop-the-Loop with Friction [closed]

Let's consider a track that begins vertically becomes a 450 degree loop, and level off. (See diagram) We drop a block from height $H$ that falls and goes around the loop. Ignoring air resistance, ...
2
votes
2answers
209 views

Mathematical model for this graph of a simplified binary star system?

Unnecessary background for question: I had a school assignment asking us to relate a quadratic equation to a real life example relating to our future dream career, making sure to express the accuracy ...
2
votes
1answer
163 views

Gravitational binding energy and integrated potential energy not the same?

Before looking up the formula for the gravitational binding energy of a uniform sphere, I simply figured that the general formula for binding energy of an arbitrarily-shaped mass distribution would be ...