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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0
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1answer
62 views

What's wrong with my math in this function to update the position of a planet near a star?

Initially the code seems to work as the planet curves toward the star, but then as it should either get pulled into the star or make an orbit, it just gets pushed away in the opposite direction. What ...
0
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0answers
17 views

Figure out the component of a value in X and Y coordinates using trigonometry.

Alright. It's been long that I studied trigonometry and did Laws of Motion and Free Body Diagrams, and I was decent good at them, but somehow I am having trouble in understanding the following. Note ...
0
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0answers
18 views

A problem on Constrained Motion

Q. A particle is moving in a smooth curve under gravity and its velocity varies as the actual distance from the highest point. Prove that the curve is a cycloid. Attempt: The eq. of motion is ...
5
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0answers
34 views

Why do people prefer cosine to sine when speaking of harmonic oscillation?

In almost all of the physics textbooks I have ever read, the author will write the oscillating function as $$x(t)=\cos\left(\omega t+\phi\right)$$ My question is that, is there any practical or ...
6
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1answer
685 views

Damped Harmonic Oscillator and Response Function

This is another one of those questions that I feel like I am almost there, but not quite, and it's the math that gets me. But here goes: For a driven damped harmonic oscillator, show that the full ...
0
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1answer
28 views

solving equation in terms of $w_1$ and $w_2$

I have a a physics problem involves the following equation $$\tan(\alpha) = \frac{(w_1 + w_2)^{1/2}}{w_3}$$ from a certain set of equations that I use I derive the following equation: ...
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2answers
54 views

Practical use for negative $dt.$

I am writing a section of notes for Calculus 1 on related rates. In the section where I discuss differentials, I write that the quantity $dt$ must be nonnegative. I imagined the only reason it would ...
1
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1answer
31 views

What is the ratio of the intensities of the two sounds?

1. Suppose that a jet engine at 50 meters has a decibel level of 130, and a normal conversation at 1 meter has a decibel level of 60. What is the ratio of the intensities of the two sounds? we ...
9
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2answers
100 views

what would a planetary orbit look like if gravity had constant magnitude?

Consider a unit-mass particle that is always experiencing a single unit-magnitude force towards the origin. This is a central force, but it is not one of the familiar ones, e.g. gravity whose ...
0
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1answer
30 views

Connecting a mathematical solution to a differential equation with it's physical solution

I have seen this question in a neuroscience course: It is given after the lecture with these and these slides. I have no background in physics. However, I do know how to solve a differential ...
0
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1answer
10 views

Setting constant as a function of all the variables expect the one we integrate on

I am having trouble fully grasping the concept of setting a constant as a function of other variables: I would like to use a particular example where I could explain my thought process. Hopefully you ...
1
vote
1answer
59 views

Can a quaternionic Kähler manifold be NOT Kähler?

I have an explicit construction of the metric on the quaternionic Kähler manifold $$\mathcal M = \frac{Sp(1, 1)}{Sp(1) \times Sp(1)}.$$ Arranging the four real degrees of freedom into two complex ones ...
1
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1answer
31 views

Following a simplification of expression

I am struggling with this expression: In particular I get stuck with the simplification from the first to the second line. As far as I can see they replace $\text{m$\ell $}=\mu$. Does the new ...
0
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1answer
24 views

does a ferris wheel which turns at a constant speed have a change in angular acceleration?

I have this multiple choice question, and i don't seem to understand if A,B,C are false or true. I have the answers in the back of my book, so really i just want to know WHY they are true or false. I ...
6
votes
1answer
93 views

Symbolic manipulation inside integral

I'm an undergrad who has just completed the standard calculus sequence (1, 2, and multivariable). I've done well in the courses, however, things like the following, which is a derivation of kinetic ...
-3
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2answers
27 views

Throwing a ball upright in the Air [closed]

When an object is thrown in the air, its height above the ground is given by $$h(t) = -16t^2 + v_0t+h_0,$$ where $t$ is in seconds and $h$ is in feet and where $v_0$ is the initial velocity of the ...
-1
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1answer
34 views

Parabola Application [closed]

A cannonball when configured to be fired at a certain angle would have a parabolic path with a maximum height of $50\mathrm{m}$ and a horizontal range of $20\mathrm{m}$. If the cannonball is placed at ...
4
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3answers
67 views

How do one rigorously prove that the electric potential energy of an conducting sphere with charge $Q$ is $\frac{Q^2}{8\pi\epsilon_0R}$

How do one rigorously prove that the electric potential energy of an conducting sphere with charge $Q$ is $\frac{Q^2}{8\pi\epsilon_0R}$? Is integration the only way? Homogeneous charge distribution ...
1
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1answer
36 views

How to derive the weak form of the PDE?

I have some difficulties solving the weak form of the PDE: The proof of the preceding statement is elementary. The weak form of the PDE $\nabla \cdot (A(x) \nabla u) + \omega^2 q(x) u = 0$ for all ...
2
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2answers
48 views

Pre-calculus - Deriving position from acceleration

Suppose an object is dropped from the tenth floor of a building whose roof is 50 feet above the point of release. Derive the formula for the position of the object t seconds after its release is ...
0
votes
1answer
59 views

Inter-neighbor resistance on triangular prism

Given a triangular prism of infinite length along the X direction. A graph is formed with the set of nodes all the points on an edge of the prism with integer values of X, and the with each node ...
3
votes
2answers
511 views

Rotation matrix from an inertia tensor

I have a set of weighted points in 3D space (in fact, a molecule) and I'm trying to align the principal axes of this set with the $x$, and $y$ and $z$ axes. To do so, I've first translated my points ...
0
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2answers
95 views

Trigonometric identities — a parallel RLC circuit connected to an AC-supply [closed]

An RLC-circuit is connected to an AC-supply as in the figure below. $I_{tot}(t)=I_0sin(\omega t+\phi)$ (denoted as $I_{ges} ( t)$ in the picture), $\phi$ is the phase angle between ...
3
votes
1answer
77 views

Counter exchanging limit and integral

Background I came across this answer on Math SE which claimed it made a lot of sense to switch limit and integral. In response I came up with the following counter-examples: $\lim_{w \to 0} ...
6
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0answers
428 views

Studying quantum mechanics without physics background

I am a PhD math student, and I am wondering if I should study quantum mechanics while I don't have an undergrad background in physics. I posted this question in physics stackexchange, but there ...
0
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2answers
47 views

Why is the potential function defined differently in physics and calculus?

I am very familiar with the concept of a potential function, and potential energy, from calculus-based physics. For instance, if we have the familiar force field $\mathbf{F} = -mg \,\mathbf{j}$, then ...
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0answers
20 views

Electric circuit application of an ODE: solve $R \frac{dq}{dt} + \frac{q}{C} = V(t)$ for $q$.

An electric circuit contains a resistance $R$ and a capacitor $C$ in series, and a battery supplying a time-varying EMF $V(t)$. The charge $q$ on the capacitor therefore obeys the $$R ...
3
votes
1answer
43 views

Can I calculate the scalar potential from the electric field using: $\phi = \int \nabla \phi = - \int \vec{E}$

If I have a relation between the electric field and the radius, can I calculate the relation between the scalar potential and the radius using: $\phi = \int \nabla \phi = - \int \vec{E}$? $$\nabla ...
18
votes
7answers
2k views

Using mathematics in theoretical physics

I'm a non-mathematician who is self-studying mathematics. Although I'm very interested in mathematics, my main purpose is to apply math in theoretical physics. The problem is that when I read a ...
1
vote
1answer
34 views

Failing to calculate earth's standard gravitational parameter

I am using this equations from Wikipedia: $$\frac{4\pi^2 a^3}{T^2}=\mu$$ Where: $\mu$ = standard gravitational parameter ($\mbox{km}^3 \mbox{s}^{−2}$) $a$ = the orbiting body's semimajor axis (AU) ...
0
votes
1answer
8k views

how to calculate the angle in the x-y, y-z, x-z plane given only 3D vector direction and magnitude?

Please help me solve this. I have been thinking of all sorts of ways to solve this but can't figure out how :(. OK here's the problem: I am given a three dimensional velocity vector (I know the ...
3
votes
2answers
183 views

sum of N light sources

[sorry for the bad English] I am fond of astronomy and environment. I want to try to make a "light pollution map" but I haven't my satellites... so I use as approximation of light pollution the ...
1
vote
0answers
26 views

Creating an arbitrary state of the quantum simple harmonic oscillator [migrated]

Suppose $\mathcal{B}=\{\lvert 0\rangle, \lvert 1\rangle, \lvert 2\rangle, ... \}$ is the energy eigen-basis of a quantum simple harmonic oscillator. I want to create the state \begin{equation} ...
0
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1answer
15 views

Hamiltonian Constant on integral curves

Let $H \in C^{2}(\mathbb{R}^2)$ and let $(x(t),y(t))$ be a solution to the equations $$\frac{dx}{dt} = \frac{\partial}{\partial y} H(x(t),y(t))$$ $$\frac{dy}{dt} = -\frac{\partial}{\partial x} ...
1
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2answers
37 views

Determining movement time with uniform acceleration/deceleration

Consider some movement along a path segment $s$ with constant acceleration/deceleration (see figure below). The initial speed is $v_0$ and the final speed is $v_1$. The constant acceleration is $a$ ...
0
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0answers
20 views

When is the density matrix not diagonal?

The density matrix (density operator) in quantum mechanics is defined as $$\hat{\rho} = \sum_{i} p_i |\psi_i\rangle \langle \psi_i|\, ,$$ where the $|\psi_i\rangle$ are a full orthonormal system and ...
2
votes
1answer
36 views

Derivation of the momentum operator

\begin{align*} \langle p \rangle &= \int_{-\infty}^\infty \frac{d p}{2\pi \hbar}\, \phi(p, t)^\ast \, p \, \phi(p, t) = \int_{-\infty}^{\infty} \frac{d p}{2 \pi \hbar} \int_{-\infty}^\infty dx' ...
1
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1answer
26 views

Bezier curve and deceleration

I have a question regarding calculation of a cubic Bezier curve. I'm programming an app where in there's continuous straight line motion of a vehicle at a constant speed. (Let's call it $u$). When the ...
2
votes
1answer
30 views

Fourier transform of a Green's function

I was studying for an exam and I found this question which has caused me a bit of trouble: Given the Green's function that satisfies the equation $$\Box ...
2
votes
1answer
40 views

Mass of Ocean to Atmosphere [closed]

This is a bizarre question, but here goes... If all of the water in the oceans were boiled into steam by the newly forming molten earth, could the atmosphere retain the steam? In other words, ...
2
votes
1answer
81 views

Best multivariable calculus text for physics [duplicate]

I will soon start studying electrodynamics from Griffith's Electrodynamics. I tried to learn the math required from the first chapter but found that I couldn't understand it very well. So are there ...
0
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0answers
30 views

Decomposition of acceleration into normal and tangential components

If the velocity $v=\|\mathbf{v}\|$ of a point having position $\mathbf{x}(t)$ at time $t$ is never null, then acceleration $\mathbf{a}:=\frac{d^2\mathbf{x}}{dt^2}$ can be written ...
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2answers
100 views

What does Uncertainty principle mean?

I do not understand the idea behind Uncertainty principle: the more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa. But as I know, ...
3
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0answers
78 views

Upper bound on the Lipschitz constant of entanglement entropy

I'm looking for an upper bound for the Lipschitz constant of entanglement entropy between two subsystems with respet to the standard distance measure of pure states in the Hilbert space of the full ...
0
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1answer
35 views

Rewrite the system in the form $\dot x = Ax + bu.$

$Ml\ddot\theta = (M + m)\dot x + mL\ddot\theta = u$ $M\ddot x = u - mg\theta$ Using the variables $x_1 = \theta, x_2 = \dot\theta, x_3 = x, x_4 = \dot x$ Rewrite the system in the form $\dot x = Ax ...
4
votes
2answers
44 views

Projectile to clear a hemispherical mound

I have only just stumbled across this site a few days ago while searching for other things. This is a great resource. I have a question for nearly 30 years now when me and my friend were trying to ...
4
votes
3answers
539 views

Trying to understand the true meaning of integral and Derivative in calculus [duplicate]

I'm solving a physics question, and i just encountered some question i had no idea how to start, i just got the right answer and inside it it has something in math i never thought possible, I know ...
0
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1answer
656 views

Acceleration and Tangential Velocity Vector? <Completely Lost>

Find the resultant acceleration of a particle moving on a circle of radius 0.70 m, if its angular speed is 37 rpm and its tangential acceleration is 2.9 m/s2. Express the angle with respect to the ...
0
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0answers
53 views

Why we have to take the vector $\overrightarrow{e}$ ?

The differential equation of the balance of the momentum is $$\rho \frac{\partial{\overrightarrow{u}}}{\partial{t}}=-\rho (\overrightarrow{u} \cdot \nabla )\overrightarrow{u}-\nabla p+\rho ...
1
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1answer
24 views

Stress vector - Stress tensor

Is the definition of the stress vector the following? The stress vector is the force per unit surface. The stress tensor is the matrix $\{\sigma_{ij}(x,t)\}$ and its $(i,j)$-component is the ...