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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7
votes
2answers
512 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 ...
1
vote
1answer
3k views

How to get angular velocity from difference orientation quaternion and time?

I am using Bullet Physic library to program some function, where I have difference between orientation from gyroscope given in quaternion and orientation of my object, and time between each frame in ...
1
vote
2answers
700 views

Homework help with projectile motion

I would please like help on the following question related to projectile motion. A horizontal drainpipe 6 metres above sea level empties stormwater into the sea. If the water comes out ...
3
votes
0answers
156 views

Check my solution - Modelling of a spring with Differential Equation

I am doing some work with differential equations. I have solved the following problem but am uncertain if I'm doing it correctly. Could someone look over it for me and check if I'm doing something ...
1
vote
3answers
274 views

Diameter of wheel

If a wheel travels 1 mile in 1 minute at a rate of 600 revolutions per minute. What is the diameter of the wheel in feet ? The answer to this question is 2.8 feet. Could someone please ...
5
votes
3answers
506 views

Dimension in mathematics and physics

I have studied linear algebra and commutative algebra, there are two kinds of dimension there : the vector space's dimension and the Krull dimension. Also, in physics, dimension is also a very ...
6
votes
1answer
234 views

A particular (functional) determinant calculation

One wants to calculate the quantity, $\det'(\frac{\partial}{\partial t} - i [\alpha, ])$ where the prime on the "det" means that one wants to do a product over only non-zero eigenvalues of the ...
1
vote
4answers
102 views

Solution to a system of quadratics

I am learning about a Bell State, and am trying to show that they are entangled. I believe that the required proof is to show that the system $$\alpha_0^2+\alpha_1^2=1$$ $$\beta_0^2+\beta_1^2=1$$ ...
1
vote
1answer
1k views

Using Parametric Equations to Define the Position of an Object in Motion

What is the intuition behind the equations for the parametric equation applications below? Rather than memorize the formulas for a quiz i'd like to gain a deep understanding of them.
0
votes
1answer
486 views

Simple harmonic motion and trigonometry

Here's the question I would like help with: A particle is moving in simple harmonic motion according to $x=6\sin \left (2t+\frac{\pi }{2} \right )$. Find the first two times when the velocity ...
2
votes
1answer
119 views

How to prove the existence of the following equation?

I learned electrodynamics. According to the vector potential determination, $$ \mathbf B = [\nabla \times \mathbf A ], $$ Coulomb gauge, $$ \nabla \mathbf A = 0, $$ and one of Maxwell's equations, $$ ...
4
votes
1answer
758 views

Choosing the sign of the separation constant for a vibrating string

Suppose we have this PDE problem $$\frac{\partial^2 \psi}{\partial x^2}=\frac{1}{c^2}\frac{\partial^2 \psi}{\partial t^2}$$ $$\psi(0,t)=\psi(L,t)=0$$ It represents the vibrations of a string tightly ...
1
vote
1answer
229 views

Simple Harmonic Motion with trigonometry

I need some help with my high school maths question: A particle is moving in simple harmonic motion has speed 12m/s at the origin. Find the displacement-time equation if it is known that for positive ...
3
votes
4answers
3k views

Hydrostatic pressure on a square

Vertically inserted into the water I have a rectangle 6 feet wide and 4 feet high that is submerged under the water with 2 feet of water above it. Using a riemann sum how do I find the pressure? I ...
-3
votes
3answers
1k views

Hydrostatic pressure on a triangle

I am attempting to follow Paul's calculus notes, but am having trouble, in particular at this page: http://tutorial.math.lamar.edu/Classes/CalcII/HydrostaticPressure.aspx I get to the part with the ...
0
votes
3answers
7k views

Centroid of a region

$$y = x^3, x + y = 2, y = 0$$ I am suppose to find the centroid bounded by those curves. I have no idea how to do this, it isn't really explained well in my book and the places I have looked online ...
2
votes
2answers
478 views

Trigonometry in Simple Harmonic Motion

In one of my high school maths questions the example given to find the maximum displacement of a Simple Harmonic Motion where $ x=2+4\cos \left (2t + \frac{\pi}{3} \right ) $ and the motion lies in ...
5
votes
2answers
2k views

Line Integral, Work in physics

Hi there all: I have a problem! I need to find the work done on a particle that moves from $(0,0)$ to a point $(1,1)$ by a strait line $y=x$. The force acting upon the particle is $F = (y , 2x$). ...
3
votes
4answers
1k views

Multivariable Calculus Book Reference

I am looking for a multivariable calculus book that is really physics oriented. Anyone know of any? EDIT: My wife is looking to brush up on multivariable at the same time she needs to brush up on ...
1
vote
2answers
1k views

Intensity of sound wave question

The question is: The intensity of sound wave A is 100 times weaker than that of sound wave B. Relative to wave B the sound level of wave A is? The answer is -2db I tried doing (10dB)Log(1/100) but ...
1
vote
1answer
986 views

Moment of inertia - formula derivation: Missing $\frac{1}{2}$

I'm trying to deduce the formula of the moment of inertia of an object of rotation. The general formula for the moment of inertia is declared as: $$J=m*r^2 =\sum{m_i * r_i^2}$$ If I replace $m_i$ ...
1
vote
1answer
860 views

Limits of integration after change of variable in higher dimensions

If we make a change of variable in higher dimensional integrals how do we decide the limits of integration. In two dimensions the problem is fairly simple using a geometric interpretation but in 3 and ...
1
vote
0answers
68 views

Stochasticity of Fermi problems

The great physicist Enrico Fermi was known for his ability to make good guesses with little or bad data by multiplying series of estimates. 1 I've seen this described as corresponding to a stochastic ...
0
votes
1answer
308 views

Implicit Differentiation Step Explanation

I'm trying to follow some notes on beam mechanics, and there is a differentiation step I don't understand. He goes from: $M_n(\lambda(1-R)+R) = \frac{1}{3} + \frac{(R-1)(1-\lambda)^2(2+\lambda)}{6}$ ...
0
votes
1answer
374 views

Is there a difference between shape geometry and spatial geometry in the universe?

My friend posed the question: "How can we construct a 4-dimensional shape [such as the tesseract, the 4-dimensional analog of the cube] when the 4th dimension is time?" My answer was that surely ...
4
votes
1answer
511 views

Method of image charge for ellipse

If we put an external electron outside a elliptical metal described by: $$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$, how do we determine the image charge or charges of that electron inside this ellipse?
3
votes
1answer
91 views

Function space in QM

I need to understand how one can think of a function as a vector (in Hilbert space, more specifically) so I can follow along QM texts. I've read this question's answers, but they were uninspiring to ...
65
votes
4answers
74k views

Teenager solves Newton dynamics problem - where is the paper?

From Ottawa Citizen (and all over, really): An Indian-born teenager has won a research award for solving a mathematical problem first posed by Sir Isaac Newton more than 300 years ago that has ...
1
vote
1answer
160 views

The Law of Sines and a second forces magnitude

How do you solve for the second forces magnitude? The 17' and 30' threw me off.
1
vote
0answers
196 views

The wave equation in action

The vibration of a piano string is governed by the wave equation $u_{tt} - c^2u_{xx} = 0$ where $c$ is related to the tension and the mass density. Suppose a string is hit by a hammer on the interval ...
6
votes
3answers
393 views

A general pattern to find the roots of the classical lie algebras

Is there any general pattern for the roots of each of the classical lie algebras? So, can I tell all the roots of each of the $nth$ rank classical lie algebras $A_n, B_n, C_n, D_n$, as a linear ...
2
votes
2answers
124 views

Is this a one dimensional Lorentz Boost? And can you have a 1-d Boost without group structure?

Someone has claimed that he has constructed a quaternion representation of the one dimensional (along the x axis) Lorentz Boost. His quaternion Lorentz Boost is $v'=hvh^*+ 1/2( ...
2
votes
1answer
2k views

Vector ODE: how to solve?

In developing a particle system simulator, I ended up with this apparently innocuous vectorial differential equation: $m \vec v\,' = -\mu \vec v + \alpha \vec v / |\vec v|$ Where $\vec v = \vec ...
3
votes
0answers
122 views

Stability of Orbits in Schwarzschild Spacetime

I'm looking at geodesics in the Schwarzschild geometry, and have come up against something I cannot prove. I've shown that for a particle moving on a geodesic with $r$ constant and $\theta=\pi/2$ we ...
0
votes
2answers
370 views

Is this proof that SU(2) cannot be isomorphic to SO(1,3) valid?

It seems intuitively obvious to me that there cannot be an isomorphism between $\mathrm{SU}(2)$ and $\mathrm{SU}(2)\times\mathrm{SU}(2)$ where SU(2) is the Lie Group with the Pauli matrices as ...
2
votes
2answers
587 views

General Relativity - Proper Time

Suppose we are working with the signature (- + + +). Then $\mathrm{d}s^2=-1,1,0$ for timelike, spacelike and null curves respectively. We define proper time by $\mathrm{d}\tau^2=-\mathrm{d}s^2$. ...
2
votes
2answers
110 views

What is the $x(t)$ function of $\dot{v} = a v² + bv + c$ to obtain $x(t)$

How to solve $$\frac{dv}{dt} = av^2 + bv + c$$ to obtain $x(t)$, where $a$, $b$ and $c$ are constants, $v$ is velocity, $t$ is time and $x$ is position. Boundaries for the first integral are $v_0$, ...
3
votes
2answers
717 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 ...
1
vote
1answer
738 views

del operator - partial derivatives

I'm taking a class in Electromagnetism, and I'm learning about the relationships between voltage and an electric field from Faraday-Maxwell equations. The equation I have trouble with is: $$E = ...
1
vote
1answer
92 views

Probabilistic interpretation of $\sum_{n \geq 0}\mathrm P_{n}(t)= 1$

The following is a problem from Spiegel's Applied Differential Equations: The probability $\mathrm{P}_{\mathrm n}(t)$ that a counter (such as a Geiger counter) will register exactly $\mathrm n$ ...
12
votes
3answers
459 views

Why can't you simulate isotropic fluid flow on a square lattice?

There are easy methods for discrete simulations of gas dispersion in two dimensions. If you take a large square lattice, each cell of which is assumed to contain at most one gas molecule, and you ...
6
votes
0answers
109 views

Analytic caustics for 3D objects

Is it possible to efficiently calculate caustics for a given 3D object, like a torus, or a cube? To be more precise: let's assume that we have a 3d torus, resting on a 2d plane and a single light ...
0
votes
2answers
238 views

velocity confusion

A velocity encompasses both speed and direction in a single vector. I'm a little bit confused about how to separate the two. I have 2 creatures. The first is located at position (x1, y1). The second ...
2
votes
1answer
79 views

How do I figure out the speed of a jet of water in this example?

I should know how to do this but I don't. I'm not very familiar with vectors. Perhaps I will be after this. So I have a stream of water falling out of a pipe. It obviously forms a parabola of the ...
7
votes
1answer
821 views

Physical interpretation of the generating function for the Bessel functions.

It is well known that the generating function for the Bessel function is $$f(z) = \exp \left (\frac12 \left (z - \frac1z \right ) w \right ).$$ So, we have $$f(z) = \sum_{\nu = -\infty}^{\infty} ...
3
votes
1answer
330 views

How to construct and oscillation with exponentially growing period times?

I'm searching for the (maybe even smooth) "oscillating" function $$f(t)=A\sin{\left(g(t)\right)},$$ such that there are zeroes at times $t_n=T^n$ for some fixed number $T$. So this will not really ...
37
votes
3answers
4k views

Intuitive reasoning behind $\pi$'s appearance in bouncing balls.

This video is about an interesting math/physics problem that when cranked out churns out digits of $\pi$. Is there an intuitive reason that $\pi$ is showing up instead of some other funky number ...
4
votes
2answers
541 views

What's the relationship between Gauss' law and Newton-Leibniz formula?

Actually it's a puzzle I got in my Physics class. Someone says Gauss' law actually is a specific example of the famous Newton-Leibniz formula, but I couldn't catch it. So far I haven't learned about ...
3
votes
1answer
409 views

Relationship between Minkowski distance and Minkowski space

The metric induced by the p-norm: $d((x_1,\dotsc,x_n),(y_1,\dotsc,y_n)) = \left(\sum_{i=1}^n |x_i-y_i|^p\right)^{1/p}$ is often called the Minkowski distance. There is also Minkowski space, which ...
8
votes
3answers
425 views

“Phase change” of a purely mathematical system

Every so often I hear people talking about "phase transitions" in purely mathematical or computer-science contexts, where there is no physics in sight. Today, for example, I heard some people talking ...