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0
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1answer
288 views

Harmonic Oscillator Energy to Momentum Expectation Value

If we are given a wave function written in terms of harmonic oscillator energy eigenfunctions how can we determine the maximum possible momentum expectation value? It's a combination of the first two ...
1
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1answer
154 views

Why does $[xp_{y},x]$ commute?

I'm looking at a solution in my book that says $[xp_{y},x]$ commutes. Does bracket notation imply: $[A,B]=AB-BA$ so that $[xp_{y},x]=xp_{y}x-xxp_{y}$ Taking the comment from Max Graves and ...
-5
votes
1answer
196 views

Classical Mechanics - Equation of motion, Lagrangian, Newtons 2nd Law [closed]

I really don't even know where to start with this question any help would go very very far. http://imgur.com/g4KxNY5
1
vote
1answer
254 views

I am unable to combine two equations in kinematics

Sorry people, very basic kinematic stuff here. (1) Velocity: $$v=\frac{d}{t}$$ (2) Acceleraton: $$a=\frac{v_{f}-v_{i}}{t}$$ (3) Re-arrange acceleration: $$v_{f} = v_{i}+at$$ (4) Ok here is my ...
1
vote
1answer
126 views

Flux increase due to velocity?

I have a book question I'm trying to understand: The first bit is easy enough. The second part I was confused so I checked the solution: B is into the page. The flux increases as the bar moves ...
1
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5answers
174 views

Is $\langle\psi_1|p\psi_1\rangle$ necessarily 0 for eigenstates? [closed]

Is $\langle\psi_1|p\psi_1\rangle$ necessarily 0 for harmonic oscillator eigenstates? If $\Psi(x,t)= c_0\psi_0(x)e^{-iE_0t/\hbar}+c_1\psi_1(x)e^{-iE_1t/\hbar}$, is the following true? Where $p$ is ...
3
votes
1answer
123 views

How do I find the expectation value given only the eigen energy? [closed]

Let $|n \rangle$ denote the $n^{th}$ stationary state of the harmonic oscillator, with energy $E_n = \hbar \omega(n+\frac{1}{2})$ How would I find $\langle x\rangle$ and $\sigma_x$ I know that ...
1
vote
1answer
133 views

Modulus Square of the Gaussian Wave Packet for uncertainty in $p$

Upon evaluating the integral (2.67) and obtaining the complex valued equation given in box 2.4, the author performs the modulus square to obtain the Gaussian distribution (2.68). How does one go about ...
4
votes
1answer
469 views

Paramagnetism Spin-1/2 Particles - Partition Function

I'm trying to come up with an expression for the partition function of a system of spin-1/2 ideal gas particles on a line of length $L$. The total number of particles $N$ is fixed, with $N = ...
0
votes
1answer
63 views

Evaluating $v$ for orbiting a golfball [closed]

The curvature of Mars is such that its surface drops a vertical distance of 2.0 meters for every 3600 meters tangent to the surface. In addition, the gravitational acceleration near its surface ...
1
vote
2answers
97 views

Does measuring the operator of a wave function collapse the wave function to the measured eigenstate?

Suppose you have a state described by the wave function $\psi(x) = \phi_1(x)+2\phi_2(x)+3\phi_3(x)$ , where the $\phi$s are normalised eigenfunctions of a Hermitian operator $\hat{O}$ with eigenvalues ...
0
votes
1answer
3k views

Rope tension between two objects [closed]

Let me explain the picture just to make sure. Object with mass 2 kg is being pulled with a force of F = 14.4 N. The whole system has an acceleration of a = 2.8 m/s^2. The friction coefficient ...
1
vote
0answers
454 views

elastic potential energy of a spring when compressed [closed]

A small ball with a mass of 1 kg rolls down a long frictionless inclined ramp, which is at an angle 30 degrees above the horizon. A linear spring, whose length is not negligible, is attached to the ...
1
vote
0answers
265 views

Rotational inertia of a sphere and a cube? [closed]

Can someone explain which would have more rotational inertia, a sphere or a cube, and why? Suppose they have the same mass, the side of the cube is equal to the diameter of the sphere, and the cube's ...
2
votes
1answer
74 views

Applying kinematics issue

I've been having an unusually difficult time solving kinematics problems in comparison to all the other students in the classroom. It appears that I'm one of the unfortunate people with an anti-math ...
1
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0answers
31 views

Cycle with unspecified irreversbile transformation. Find $P,V$ in the various states.

I've been thinking to this for the last two hours and haven't been able to come with a solution. Problem. A mole of gas initially at pressure $P_A = 2 \text { atm}$ and occupying a volume ...
0
votes
2answers
251 views

Normalising a wavefunction where $\psi$ is equal to a sum of functions [closed]

The wavefunction $\psi(x)$ = $\phi_1(x)$ + $2\phi_2(x)$ + $3\phi_3(x)$ is to be normalised. The functions $\phi_1(x)$, $\phi_2(x)$, $\phi_3(x)$ are normalised eigenfunctions of a Hermitian operator ...
-9
votes
1answer
132 views

General Physics II Practice Question [closed]

I have a test in a few hours, and my professor gave us a practice test, and I'm stuck. Could you give me a hint as to how to approach this problem, equations I could use. It's an algebra based class ...
1
vote
1answer
80 views

Show that detF(X,t) is positive in continuum mechanics?

I want to show that the determinant of the field $detF$ at the point $X \in B$ is positive, when the following motion. I think that time derivative of Jacobin is positive for $t > 0$. However, I ...
-1
votes
2answers
118 views

Harmonic Motion [closed]

A light elastic string is stretched between two points, one lying vertically below the other. A particle is attached to the midpoint of the string, causing it to sink a distance h. Assuming that the ...
2
votes
1answer
274 views

Apparent size of objects under water

A friend of mine has a homework question and we're having some trouble figuring out what physical mechanisms come into play for this. An underwater swimmer sees a spherical air bubble that appears ...
0
votes
1answer
4k views

String tension in vertical circular motion

Suppose that I have a point mass attached to a massless string and I am rotating it vertically. That means The mass is in uniform circular motion and the path of its motion is vertical circle. How ...
4
votes
1answer
219 views

What are the generators of spherical symmetry?

The title says it all. I think this should be a pretty simple question but I just couldn't find the answer. Ok -- I'll give a bit more context to my question. I'm encountering this in the context of ...
-6
votes
1answer
358 views

Are dc and ac currents produce electric field? [closed]

I have four different situation and i want to learn what kind of field (electric or magnetic) each produces and which produces electomagnetic waves? 1)dc current flow in a conductor 2)ac current ...
0
votes
1answer
202 views

Calculate the change in the Fermi energy as the temperature is raised

Sodium has a volume expansion coefficient of $15 * 10^{-5} K^{-1}$. Calculate the percentage change in the fermi energy as the temperature is raised from $T = 0K$ to $T = 300K$. My attempt at the ...
3
votes
2answers
282 views

Formulation and probability of a wave-function [closed]

I have got this problem where I have been given the following wave function: $$\Psi = 0\quad\text{if}~|x| > a\quad\text{and}\quad A(a^2-x^2)\quad \text{if} \quad |x|< a$$ Now the first question ...
2
votes
1answer
136 views

Can the Lagrange Multipliers depend on the coordinates?

When dealing with Lagrange multipliers to solve systems with constraints we usually have two ways if the constraints are holonomic: Differentiate the constraint and add the appropiate term to the ...
1
vote
1answer
215 views

Question regarding mass hanging from center edge of rotating disc

So, say you have a free to rotate disc, assuming no external torques, and you have a spool, radius 7.93 mm, attached to its centre. Say the spool has a string attached to a point on its edge and ...
2
votes
2answers
190 views

Exercise about Lagrange-Euler equations

I'm solving an exercise about the Lagrange-Euler equations, that states the following: Let $\gamma (t) = \{ (t,q) : q = q(t), t_0 \leq t \leq t_1\}$ be a curve in $\mathbb{R} \times \mathbb{R}^2$. ...
6
votes
1answer
572 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 ...
2
votes
1answer
145 views

What forces are exerted on a clothespin in space?

Let's say a clothespin is modeled as a simple torsion spring as follows. Given: $p_1,\ p_2,\ p_3$: point-like objects of equal mass in 2-D space. All objects float in space, i.e. the center of mass ...
-1
votes
1answer
185 views

Can you help me with physics lab calculations? [closed]

My question is, how do you find the torque of a rotating spool with a connected string being pulled down by its hanging mass? So in this experiment we had a machine with two rotating discs, one on ...
1
vote
2answers
155 views

Refraction of light in medium

Given that the plane $y=0$ separates the vacuum ($y>0$) from the optical medium ($y<0$), I would like to calculate the trajectory of a light ray starting at the point $(x_1,y_1)$ and ending in ...
1
vote
0answers
122 views

Density distribution of gas in a centrifugal field

The problem asks me to find the density of gas in a cylinder of radius $R$ and length $l$ rotating about its axis with angular velocity $ω$, there being a total of $N$ molecules in the cylinder. What ...
3
votes
2answers
177 views

Dimensional regularization - integral

How can I derive the following formula? $$\int d^{d+1} k \frac{e^{i K X}}{K^2} = \frac{\Gamma (d-1)}{(4\pi)^{d/2} \Gamma (d/2) |X|^{d-1}}, \quad K^2 = k_0^2 + \vec k^2, KX = k_0 \tau + \vec k \vec ...
1
vote
0answers
109 views

Torque on object [closed]

I would like to understand why the torque on white object is 0. I know gravitational forces are very low. But the torque must be at 0. I drawn all the study in first image. Blue color is a torus of ...
0
votes
3answers
102 views

$P\sin(\alpha)$ and not $\sin(\alpha)/P$?

Why is the force parallel to the surface that pushes the object $P \sin(\alpha)$ and not $\frac{\sin(\alpha)}{P}$? I didn't understand when they showed me it. can someone give me an answer in full ...
-1
votes
1answer
59 views

Centripetal acceleration and gravitational acceleration on a thread [closed]

This is a question from my physics textbook. "A $200$ gram weight is suspended in a $2.5m$ long thread in the roof. The weight is pulled out sideways, creating the angle $\alpha$ and is then ...
1
vote
3answers
4k views

Vertical and horizontal components of forces and vectors

I'm getting a bit confused when finding components of vectors and forces. In problems for vectors, I've always known that if you want to get the components of a vector, you would use the following: ...
0
votes
0answers
62 views

Faulty Uncertainty Calculations for a Ground State Particle in an Infinite Well

For the infinite well: $$U(x)=\quad\infty : x \leq 0\quad 0 : 0 < x < L\quad \infty : x \geq L$$ $\psi_n=$$\sqrt{\frac{2}{L}}\sin{\frac{n\pi x}{L}}$ Find $\Delta x_n$, the uncertainty in ...
0
votes
2answers
535 views

Quantum Commutator Identities

Question: Prove that $p^2$ and ${\bf r}\cdot {\bf p}$ commute with every component of ${\bf L}$ using the identity $$[{\bf p},{\bf e}\cdot {\bf L}]=i\hbar\, ...
0
votes
1answer
65 views

Fourier Transform of E-Field with Decay Constant

Given an atomic transition with associated E-field $E(t) = E_{0}\cos(\omega_{0}t)e^{-t/\tau}$ where $\omega_{0}$ is the natural line frequency and $\tau$ is the decay constant of the simple harmonic ...
2
votes
2answers
935 views

Proving that the hermitian conjugate of the product of two operators is the product of the two hermitian congugate operators in opposite order

I have reach a step in a problem of my quantum mechanics textbook that requires me to prove the following. $$\hat{A}=(\hat{Q}\hat{R})^{\dagger} = \hat{R}^{\dagger}\hat{Q}^{\dagger}$$ I tried to ...
1
vote
1answer
226 views

Heisenberg uncertainty principle - question [closed]

A beam of particles each having mass $m$ and velocity $v$ in the incident on a circular hole of radius $b$ located on a screen. If another screen is placed at a distance $D$ from the hole, ...
4
votes
1answer
682 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 ...
1
vote
1answer
129 views

What is the depth in meters of the pond? [closed]

A small spherical gas bubble of diameter $d= 4$ μm forms at the bottom of a pond. When the bubble rises to the surface its diameter is $n=1.1$ times bigger. What is the depth in meters of the pond? ...
-4
votes
2answers
231 views

Alternative derivation for the capacitor energy equation [closed]

I hope this is the right place for this kind of post. A friend is trying to derive the equation for the energy stored in a capacitor by analysing the change in potential on one plate when the ...
2
votes
1answer
222 views

Work done by a variable force [closed]

The question asks to find the work done by the force $\mathbf{F(t)}=(4\mathbf{i}+12t^2\mathbf{j})N$ in the time interval $0\leq{t}\leq{1}$ on a particle of mass $4kg$, however I am not sure my working ...
-2
votes
2answers
324 views

Explain what happens to object in lift [closed]

In the following image,three cases have been mentioned. $N$ is the normal force acting on the object inside the lift and $mg$ is the force of attraction due to gravity. In case 1, $N = mg$. In case ...
2
votes
2answers
341 views

Doppler effect problem with moving mirror

This was the given question: A light beam of intensity $I$ and frequency $f$, directed along the positive $z$-axis, is reflected perpendicularly from a perfect mirror which itself is moving ...