Applies to questions of primarily educational value - not only questions that arise from actual homework assignments, but any question where it is preferable to guide the asker to the answer rather than giving it away outright.
3
votes
1answer
716 views
How do I construct the $SU(2)$ representation of the Lorentz Group using $SU(2)\times SU(2)\sim SO(3,1)$ ?
This question is based on problem II.3.1 in Anthony Zee's book Quantum Field Theory in a Nutshell (I'm reading this for fun- it isn't a homework problem.)
Show, by explicit calculation, that ...
3
votes
2answers
1k 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?
...
3
votes
2answers
186 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 ...
3
votes
2answers
119 views
Find work done by force along a path - is parameterization the only way?
$F = x^3y^4 \hat i + x^4y^3 \hat j$ from $(0,0)$ to $(1,1)$.
I am given different paths.
For example, "first along x axis and then along the y axis" is one of the paths.
Is this problem solvable ...
3
votes
2answers
125 views
Metric coefficients in rotating coordinates
Let $(t,x,y,z)$ be the standard coordinates on $\mathbb{R}^4$ and consider the Minkowski metric
$$ds^2 = -dt^2+dx^2+dy^2+dz^2.$$
I am trying to compute the metric coefficients under the change of ...
3
votes
2answers
220 views
Necessary air pressure in flexible vessel to lift a certain mass
I have the following situation in mind:
A big airtight bag of arbitrary shape with a person standing on it. The bag gets inflated with air to lift the person.
Assuming that the bag is much larger ...
3
votes
3answers
758 views
How can I determine density of a gas only given temperature?
I have a homework problem where exhaust is traveling through an exhaust system (assumed to be air for simplicity) from and engine and then released into the atmosphere. The exhaust is at a temperature ...
3
votes
3answers
171 views
How to compute the speed necessary for an airplane to fly?
I give some physics lessons to a friend. She asked me a question that I am unable to answer. Could you help me ?
A plane has a weight of $2\times10^6$kg. The surface of the wing is $1200 \text{m}^2$. ...
3
votes
2answers
461 views
Electrostatic Pressure Concept
There was a Question bothering me.
I tried solving it But couldn't So I finally went up to my teacher asked him for help . He told me that there was a formula for Electrostatic pressure ...
3
votes
3answers
402 views
Momentum and Energy in Oscillations
During oscillatory motion, whether it's a simple pendulum, a block on a spring, or liquid sloshing back and forth in a well...
Is energy or momentum or both conserved? Why?
Is energy or momentum (or ...
3
votes
2answers
197 views
Hydrostatics: Log floating in water near a dam
So I am studying for a final and can't seem to solve this. There is a log floating in water and I need to find its weight. The question I have is what parts of the volume of the log count when summing ...
3
votes
2answers
112 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
2answers
316 views
Paramagnet: Negative specific heat?
for a simple paramagnet ($N$ magnetic moments with values
$-\mu m_i$ and $m_i = -s, ..., s$) in an external magnetic field $B$, I have computed the Gibbs partition function and thus the Gibbs free ...
3
votes
1answer
43 views
Why doesn't this equation for orbital motion change with position in the orbit?
The question and answer are on pg.8-10 of this PDF:
At first, I went through it, thinking nothing of it. But then, I wondered: "What if we picked a final state in which the space junk was NOT at ...
3
votes
2answers
115 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
2answers
38 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 $x=a\sin(\omega t)$. ...
3
votes
2answers
117 views
Quantum commutator
I'm given this commutator:
$$\left[PXP,P\right]$$
Being $P\psi=-i\hbar\partial_x\psi$, and $X\psi=x\psi$
I've solved it in two ways, the first one is just aplying the commutator to some function ...
3
votes
3answers
117 views
Relation between the determinants of metric tensors
Recently I have started to study the classical theory of gravity. In Landau, Classical Theory of Field, paragraph 84 ("Distances and time intervals") , it is written
We also state that the ...
3
votes
1answer
87 views
How deep is the well, given this data?
A rock is dropped into a well. A timer starts when the rock is dropped and is stopped when the noise of the rock hitting the ground of the well is heard. How deep is the well?
Here's what I have so ...
3
votes
2answers
581 views
Electric field and electric potential of a point charge in 2D and 1D
in 3D, electric field of a piont charge is inversely proportional to the square of distance while the potential is inversely proportional to distance. We can derive it from Coulomb's law.
however, I ...
3
votes
2answers
190 views
Projectile motion along the earth
Suppose a projectile is launched from the Earth's surface with initial velocity $v_0$ well below speed of light and initial angle $\theta_0$ with respect to the vertical line perpendicular to the ...
3
votes
2answers
213 views
How to measure g using a metre stick and a ball
Can I measure the value of g using only a metre stick and a ball? I am not supposed to use a stopwatch and that has been the problem.
NOTE: I do not know if a solution exists or not.
3
votes
1answer
274 views
Finding the tension in rope tied to ladder using the principle of virtual work
A ladder $AB$ of mass $m$ has its ends on a smooth wall and floor (see figure). The foot of the ladder is tied by an inextensible rope of negligible mass to the base $C$ of the wall so the ladder ...
3
votes
1answer
248 views
QED BRST Symmetry
This is a homework problem that I am confused about because I thought I knew how to solve the problem, but I'm not getting the result I should. I'll simply write the problem verbatim:
"Consider QED ...
3
votes
2answers
909 views
Conservation of Momentum/Energy collision Problem
I'm working on a physics problem in preparation for the MCAT and there's this particular problem that's troubling me. I don't know if it's a bad question or if I'm not understanding some sort of ...
3
votes
1answer
538 views
Escape velocity of a rocket standing on Ganymede (Moon of Jupiter)
I want to calculate the escape velocity of a rocket, standing on the surface of Ganymede (moon of Jupiter) and trying to leave Ganymede.
My thinking was, the kinetic energy $E_{\text{KIN}}$ must be ...
3
votes
2answers
261 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
446 views
Complete vs General Integral of first order PDE
The following is an excerpt from Landau's Course on Theoretical Physics Vol.1 Mechanics:
... we should recall the fact that every first-order partial differential equation has a solution depending ...
3
votes
3answers
359 views
D'Alembert's Principle: Where does $-Q_j$ come from?
This is a follow-up question to D'Alembert's Principle and the term containing the reversed effective force.
From the second term of Eq. (1.45)
$$\begin{align*}
\sum_i{\dot{\mathbf{p}}_i \cdot ...
3
votes
2answers
649 views
What potential energy functions are mostly used in Schrodinger equation?
In the time-independent Schrodinger equation
$$\left(-\frac{\hbar^2}{2m}\Delta+V(\mathbf{r})\right)\psi(\mathbf{r})=E\psi(\mathbf{r})$$
What functions $V(\mathbf{r})$ are mostly used in research ...
3
votes
1answer
138 views
Schrödinger equation for a harmonic oscillator
I have came across this equation for quantum harmonic oscillator
$$
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
3answers
88 views
Does a cross really have a smaller area moment of inertia than a square of the same area?
I need to calculate the area moment of inertia of a cross for a homework assignment. The cross is a symmetric plus sign:
_
| |
|== ==|
| |
-
...
3
votes
1answer
203 views
Galaxies moving away at the speed of light
As an arts student, I really find those cosmological questions hard to understand and hence come here to seek your kind help.
The Hubble constant $H_0$ is estimated to be about 65 km/s/Mpc, where 1 ...
3
votes
1answer
83 views
Simple pendulum period in three different cases
Imagine you have a simple pendulum hanging on the ceiling of a train which has a period called T. How will the period be in the following cases:
When the train is in circular motion in a curve of ...
3
votes
2answers
131 views
Space Quantization of Quantum Angular Momentum
I am trying to understand what my book is trying to convey.
Quantum angular momentum is $L_z = m_l \hbar$
"Choosing arbitrarily a z axis and using an appropriate experimental technique, we measure ...
3
votes
1answer
404 views
Differences of behaviour of a particle in a box in quantum theory between that in classic physics
Can anyone help me enlist 3 major differences between the quantum and classical physics of the behaviour of a particle in a box? I would like some insight into the differences without solving PDEs ...
3
votes
1answer
134 views
Quantum computing problem
Suppose that a qubit is in the state $|\varphi\rangle=a|0\rangle+\sqrt{1-a^2}|1\rangle$, where $a\in[-1,1]$.
If we first perform a standard basis measurement on this qubit and then perform a
...
3
votes
2answers
316 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
125 views
Spin-orbit coupling constant for rubidium
I have come across the following question in my course notes:
The $5s\to 5p$ transition in rubidium is split into two components with wavelengths of 780nm and 795nm respectively. For the $5p$ state, ...
3
votes
1answer
552 views
Electric Potential of a Charged Sphere
Problem Consider a sphere with radius $R$, and with a charge distribution $\rho(r)=\rho_0r$. Using Poisson's equation, calculate the electric potential inside and outside the sphere.
Solution I don't ...
3
votes
2answers
942 views
Does Earth's Rotation Affect Its Shape?
The question I am working on is, "Consider the following.
(a) Find the angular speed of Earth's rotation about its axis. rad/s
(b) How does this rotation affect the shape of Earth?"
I am fully ...
3
votes
1answer
106 views
Inner product of particle-anti-particle spinor components
Suppose I have four-component spinors $\Psi$ and $\bar \Psi$ satisfying the Dirac equation with
$$\Psi(\vec x) = \int \frac{\textrm{d}^3 p}{(2\pi)^3} \frac{1}{\sqrt{2 E_{\vec p}}} \sum_{s = \pm ...
3
votes
1answer
230 views
Finding the diameter a parachute must be to land a probe on Mars at specific speed
Hi I'm trying to solve this textbook example but I don't know where to begin;
NASA has decided to send an experimental probe to Mars. Its weight on earth is $40 kg_f$. When the probe is near ...
3
votes
2answers
71 views
possible values of quantity in matrix mechanics
Suppose that there is a quantity described by the matrix as the following:
$M = \begin{bmatrix} 3 & 0 & -i \\ 0 & 1 & 0 \\ i & 0 &3\end{bmatrix}$
How we determine possible ...
3
votes
4answers
2k views
Calculating impact force for a falling object?
Good evening, I'm trying to calculate what kind of impact force a falling object would have once it hit something. This is my attempt so far:
Because $x= \frac{1}{2} at^2$, $t=\sqrt{2x/a}$
$v=at$, ...
3
votes
2answers
147 views
Which equation tells you the minimum energy of a wave needed to see a small particle?
I have a problem that asks for the minimum energy of a wave that we will use to see a particle of size $.1\text{ nm}$. I understand that I can not see a $.1\text{ nm}$ particle with any wave length ...
3
votes
1answer
158 views
Wick Order and Radial Ordering in CFT
I am not so much familiar with the computations tools of conformal field theory, and I just run into an exercise asking to demonstrate the following formula (related to the bosonic field case):
...
3
votes
3answers
361 views
A freefalling body problem, only partial distance and time known
Well, I've been trying to figure out a problem which I imposed on myself, so no literal values included. Unfortunately, my brain is not cooperating.
The problem states:
What is the height from ...
3
votes
1answer
309 views
Compound lenses and virtual images
Ok so I have this problem where I have a system of two lenses. All I know is that the distance between the object and the first lens is 30cm, the distance between the object and the final image is ...
3
votes
2answers
373 views
How do I calculate the position on the Bloch sphere of a quantum gate with a given diagonal matrix?
In quantum computation there are several principal quantum gates that have corresponding matrix representations. One of these is the Z gate, whose matrix is $\left[\begin{smallmatrix} 1 & 0 \\ 0 ...
