Questions related to mathematical physics which include application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories

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6
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2answers
326 views

Novel approaches to elementary number theory and abstract algebra

As a part of a university course, I'll have to study Herstein's Topics in algebra and Hardy&Wright's Introduction to the theory of numbers. Can you suggest some books (to be used as companions) ...
1
vote
0answers
60 views

Diagonalization of total angular momentum over creation operators for an isotropic harmonic oscillator?

You have an isotropic three dimensional quantum harmonic oscillator so the Hamiltonian is $$ H=\frac{p^2}{2}+\frac{r^2}2 $$ If you do the creation-annihilation operator-algebra trick and define ...
0
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1answer
22 views

Simple Harmonic Question regarding acceleration

I would just like to clear something up in regards to acceleration in SHM. When a question asks to find maximum acceleration, why do the solutions require you to use the absolute value of ...
0
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0answers
9 views

Rotation of an object's acceleration

I want to track things that can rotate using acceleration. The visual involves overlaying two graphs rotated at different angles. This is needed because the accelerometer also rotates with the ...
5
votes
2answers
40 views

Find $J: S^2\rightarrow \mathbb{R}$, if given $I:S^2\rightarrow \mathbb{R}$, s.t. $I(\vec{a})=\int_{S^2}\vec{n}\cdot\vec{a} J(\vec{n}) ds$.

I thought of the following problem, when we were discussing radiation intensity in an astrophysics lecture. Suppose $\mathbb{R}^3$ is filled with uniform radiation, i.e. there is a function ...
1
vote
1answer
32 views

Books for Tensor Algebra used in Physics?

I'm taking a dual Math,Physics undergraduate course.I want to study GR and a few parts of relativistic Quantum Mechanics.I've a decent amount of knowledge in linear algebra. Though we have tensor ...
0
votes
1answer
24 views

Question about Maximum Principle

I'm just learning about the maximum principle in my PDE class. I thought I'd be able to apply it to something else I was learning about in electrostatics (namely, that the surface of a conductor is ...
0
votes
2answers
24 views

System of equations, how to do this

This is for a physics class, but I think the question is mathematical in nature. We have the following equations: $$ \mu (c-c') = -m(v-v')$$ $$ \mu (c^2 - c'^2) = -m(v^2-v'^2) $$ $$ c+ c' = v + ...
0
votes
1answer
69 views

Calculate maximum possible velocity, given D, V0, A, J

I'm writing a program that controls space ship. I needed to determine total travel time for the following scenario: ship has some initial velocity V0 ship needed to travel distance D with maximum ...
0
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0answers
17 views

Heinrich Hertz on Mathematical Equations

What is the quote from Heinrich Hertz on how he could never exhaust the meaning behind a mathematical equation? (It's not mentioned in the Hertz quotations here.)
0
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1answer
21 views

one-dimension motion

A rock is thrown vertically up at 80 ft/s. Find it's maximum height, time of flight, and final velocity as it passes the starting point. So for my parameters I have: initial y=0 final y=? ...
1
vote
1answer
33 views

Prove $ \nabla \cdot (f \nabla \psi ) = \nabla f \cdot \nabla \psi + f \nabla ^2 \psi $ in general curvilinear coordinates.

Prove $ \nabla \cdot (f \nabla \psi ) = \nabla f \cdot \nabla \psi + f \nabla ^2 \psi $ in general curvilinear coordinates. I have been attempting to do this using general curvilinear dot products ...
1
vote
0answers
14 views

Specific volume of an air parcel

So I have an unsaturated air parcel in the atmosphere that ascends adiabatically from the $1000$ mb level to the $700$ mb level with its initial temperature being $10$ degrees Celsius. I have to find ...
1
vote
3answers
37 views

Acceleration to speed at specific distance and time

My brain hurts and I'd really appreciate some help with this formula. I am currently at 0m travelling 50m/s. I want to decelerate and come to a stop at 10m in exactly 0.5 seconds. What should be my ...
0
votes
1answer
107 views

Finding total work by integration

The following tank is completely filled with water. Find the total amount of work done in pumping water out of the outlet. Note that the density of water is 1000 kg/m$^3$ I feel like I am ...
0
votes
0answers
38 views

HyperCube questions

I have three hypercube questions. 1) How many nodes does a d-dimensional HyperRing have (as a function of d) ? 2) How many edges ? 3)What is the degree of each node in a HyperRing with n nodes ? I ...
1
vote
1answer
19 views

Find the average acceleration

Find the average acceleration of the tip of the 2.4-cm long hour hand in the interval noon to 6pm. I found the average velocity is -2.2x10^6 but I'm not sure how to go about finding acceleration. If ...
0
votes
1answer
35 views

help setting up a velocity question

Standing on the ground from 3.0 m from a building, you want to throw a package from your 1.5- shoulder level to someone in a window 4.2 m above the ground. At what speed and angle should you throw ...
0
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0answers
35 views

Solution to Laplace's Equation in different coordinate systems

Find the general solution to Laplace's equation for spherical symmetry (everything can only depend on $r$, the radius), cylindrical symmetry (everything can only depend on $s$, the radius), and planar ...
0
votes
0answers
58 views

Relative motion question

You wish to row straight across a 63-m-wide river. You can row at a steady 1.3 m/s relative to the water, and the river flows at 0.57 m/s. I know I need to draw a right triangle for the question but ...
1
vote
1answer
43 views

List of well-known submodular function in physics, statistics, math?

Can you please share a list of well-known submodular functions (have the diminishing return property) that you know? In physics, stats, math, etc? I am searching for a submodular function for my ...
1
vote
1answer
27 views

The weight of a drilled out cylinder

Cylinder is $2.71$kg or $2710$g, diameter is $5$cm and $7.5$cm high. The volume is $147.18$cm$^3$ and the density is just the mass divided by the volume, I'm not sure if I need to convert it into ...
1
vote
1answer
197 views

Work on Springs using Hooke's Law

I'm currently stuck on parts c and d of this problem. The problem says Suppose a force of 20 N is required to stretch and hold a spring 0.4 m from its equilibrium position (0). I found k constant to ...
2
votes
1answer
57 views

Quantum translation operator

Let $T_\epsilon=e^{i \mathbf{\epsilon} P/ \hbar}$ an operator. Show that $T_\epsilon\Psi(\mathbf r)=\Psi(\mathbf r + \mathbf \epsilon)$. Where $P=-i\hbar \nabla$. Here's what I've gotten: ...
5
votes
3answers
198 views

Intuitively, how do you explain the concept of Flux?

Lately in my physics and mathematics classes, I've come across the concept of Flux. And although I've been able to define them mathematically and figure out how to use them. I'm still not entirely ...
0
votes
2answers
29 views

Why write the solution of the harmonic oscillator form 1 is equal to writing form 2?

Why write the solution of the harmonic oscillator form $$\psi=A\cos\omega_0 t+B\sin \omega_0t$$ is equal to writing form $$\psi=C_1e^{i\omega_0t}+C_2e^{-i\omega_0t}$$? I would like to see how one ...
0
votes
1answer
42 views

Quadratic problem

NASA launches a rocket at $t = 0$ seconds. Its height, in meters above sea-level, as a function of time is given by $h(t) = -4.9t^2 + 37 t + 101$. Assuming that the rocket will splash down into the ...
1
vote
4answers
84 views

Products of Infinitesimals

In my physics class my professor was abusing the derivative, as per so many physics classes I've been in. This time, he took the quantity $(x+dx)(y+dy)$ and argued that the $dxdy$ term should ...
1
vote
2answers
22 views

Newton 2nd law for rotations: $\tau = I \alpha$ dimensions correct?

I have a really stupid question, which I can't figure out at the moment. I don't see why the following is correct when you check the dimensions: $\tau = I \alpha \;\;\rightarrow \mathrm{Nm= kg ...
0
votes
0answers
23 views

rabbit and Tortoise

A hare (rabbit) and a tortoise (turtle) are in a foot race. When the tortoise is 22 m from the finish line, he has a speed of 4.0 m/s but is 5.0 m behind the rabbit. The rabbit has a speed of 5.0 m/s. ...
0
votes
2answers
28 views

How to calculate the direction (of velocity of a ball) after collision with another ball?

Say I have two balls of same radius, in the 2-D Plane. So like a pool (billiard) game. I have the cue ball, moving with the velocity vector V, the magnitude is not important, so we only need an angle ...
2
votes
0answers
59 views

Forced oscillation in a pendulum and resonances

In a pendulum without the small angles approximation the equation describing the motion of the mass is: $$\ddot{\phi}(t)=-\dfrac{g}{l}\sin\left(\phi(t)\right)$$ Applying a sinusoidal force ...
0
votes
0answers
38 views

Solving the integral to calculate the electrostatic force between two tubes

Let's say we have two tubes with charges $q_1$, $q_2$, radii $b_1$, $b_2$ and lengths $l_1$ and $l_2$. They are placed along the surface of each other like in this figure: To calculate the ...
1
vote
1answer
76 views

Solving the equation of damped oscillator

I'm asked to prove that any solution of the equation $$\ddot\Phi+\Gamma\dot\Phi+\omega_0^2\Phi=0;\qquad \omega_0>\frac\Gamma 2$$ is $$\Phi=A_0e^{-\frac{\Gamma}{2} t}e^{i(\omega t-\beta)};\qquad ...
0
votes
0answers
48 views

Testing Divergence Theorem using Spherical Coordinates

I'm trying to verify the divergence theorem using spherical coordinates for the vector field $\vec{F}=r^2cos^2\theta(cos\theta\hat r-sin\theta\hat\theta)$ through the top half of the unit sphere. ...
5
votes
1answer
72 views

Show that the profile of the hill is a cycloid

I'm struggling with this problem: From George Simmons_ Differential Equations At sunset a man is standing at the base of a dome-shaped hill where if faces the setting sun. He throws a rock ...
3
votes
1answer
154 views

Find vector field given curl

I have an equation $\nabla \times \vec{B} = \mu_{0}\vec{J}$, where $\vec{J} = \left\langle f(x,y), g(x,y), 0 \right\rangle$ and need to solve for $\vec{B}$. I've looked elsewhere on here for how to ...
1
vote
3answers
749 views

Center of Mass in 3D object?

How would I find the center of mass in a 3D object (a "spinning top" or "dreidel") that consists of a cylinder welded on top of a box welded on top of an upside down cone? Assume building material is ...
1
vote
0answers
51 views

How can I calculate the force that is applied on a tube by an another tube?

Let's say there is two tubes (cylinders with no tops or bottoms) with charges $q_1$ and $q_2$, radii $b_1$ and $b_2$, lengths $\ell_1$ and $\ell_2$. These tubes are located along the axis of each ...
0
votes
1answer
41 views

How to find time it takes for an object to slide on an incline ramp [closed]

So I hope I am asking this question in the correct spot. Here is my question: if there is an incline at $70$ degrees, the object's friction is $\mu = 0.1$, and the incline is $1$ meter long, how long ...
2
votes
1answer
204 views

When does a particle with given acceleration change the direction of motion?

A particle moves along the x-axis so that its acceleration at any time $t\geq0$ is given by $a(t)=12t-4$. At time $t=1$, the velocity of the particle is $v(1)=7$ and its position is $x(1)=4$. ...
0
votes
2answers
25 views

Finding vertical displacement

I am being asked to find the distance a shuttle travels upward after a given amount of time. I know that time passed is 79s, the rate of acceleration is 6.244 m/s^2, and the speed at 79s is 493.276 ...
3
votes
1answer
61 views

How to mathematically determine if the magnitude of a cross product is up/down(positive/negative?)?

So, I'm a newbie at complex vector math. I'm working on a 2D physics engine, and my issue is, with angular acceleration from torque, is it supposed to be positive or negative? I understand the right ...
2
votes
2answers
124 views

Find the work done by the force field in moving the particle from one point to another

Find work done by the force field F in moving the particle from $(-1, 1)$ to $(3, 2)$ This sounds good till we are given that $\textbf{F} = \dfrac{2x}{y}\textbf{ i }- \dfrac{x^2}{y^2}\textbf{ j }$ ...
0
votes
1answer
20 views

Simplifying $\frac1{gt}\sqrt{g/2h}\,dx$ in free fall equations

The relevant equation: $x(t) = \frac12 gt^2$ , $dx/dt = gt$ , $T=\sqrt{2h/g}$ $dt/T = (dx/gt)\sqrt{g/2h} = 1/(2\sqrt{hx}) dx $ I do not see how $(dx/gt)\sqrt{g/2h}$ turns into $1/(2\sqrt{hx}) dx $ ...
1
vote
2answers
86 views

Water Refraction and the depth of the water.

I'm not sure if this is the right place to ask my question! But I hope I will find some help!. Image distortion occurs by refraction of light at the boundary surface between air and water when a ...
1
vote
1answer
55 views

How do component wavelengths *add* to wavelength of light color?

Say you have 3 leds at frequencies (or wavelengths) $u_1, u_2, u_3$ in Hz (or nm). Then how do you calculate the apparent or center of, or blah frequency (I don't know what I want really) of the ...
0
votes
0answers
42 views

Using significant figures, what would the answer be?

I've been learning about significant figures and I have a few questions. When you multiply/divide, the number of significant figures in the answer should be the same as the term with the least number ...
2
votes
1answer
56 views

Why does a heating model work?

I am referring to: $T=T_0 e^{kt}$ where T=temperature,t=time and k=constant. It seems to work, I as just curios to why it works?
0
votes
1answer
63 views

How to calculate the area of a 4 dimensional curve?

I have been searching on Google about it, and I found that given a sample, 4 points, per example, I could find a function and use integral on it. I am sorry if it sounds silly, I am very dummy in ...