# Tagged Questions

For questions about problems related to physics that involve evaluating integrals. Purely mathematical questions should be asked at math.SE.

41k views

### How to get distance when acceleration is not constant?

I have a background in calculus but don't really know anything about physics. Forgive me if this is a really basic question. The equation for distance of an accelerating object with constant ...
567 views

### Why we use $L_2$ Space In QM?

I asked this question for many people/professors without getting a sufficient answer, why in QM Lebesgue spaces of second degree are assumed to be the one that corresponds to the Hilbert vector space ...
1k views

2k views

### Integrating radial free fall in Newtonian gravity

I thought this would be a simple question, but I'm having trouble figuring it out. Not a homework assignment btw. I am a physics student and am just genuinely interested in physics problems involving ...
2k views

### When is Lebesgue integration useful over Riemann integration in physics?

Riemann integration is fine for physics in general because the functions dealt with tend to be differentiable and well behaved. Despite this, it's possible that Lebesque integration can be more ...
6k views

### How do you do an integral involving the derivative of a delta function?

I got an integral in solving Schrodinger equation with delta function potential. It looks like $$\int \frac{y(x)}{x} \frac{\mathrm{d}\delta(x-x_0)}{\mathrm{d}x}$$ I'm trying to solve this by ...
394 views

### Trajectory of a photon around a Schwarzschild black hole?

Consider a photon coming from the infinity in a unbounded orbit to a Schwarzschild black hole (Schwarzschild radius $r_{s}$) (see this for illustration). Its impact parameter is $b$ and its distance ...
963 views

### Electrostatic energy integral for point charges

The electric energy stored in a system of two point charges $Q_1$ and $Q_2$ is simply $$W = \frac{1}{4\pi\epsilon_0}\frac{Q_1Q_2}{a}$$ where $a$ is the distance between them. However, the total ...
10k views

### Wrong calculation of work done on a spring, how is it wrong?

So I would have thought that this would be how you derive the work on a spring: basically the same way you do with gravity and other contexts, use $$W=\vec{F}\cdot \vec{x}.$$ If you displace a spring ...
177 views

### Recovering QM from QFT

Reading through David Tong lecture notes on QFT. On pages 43-44, he recovers QM from QFT. See below link: QFT notes by Tong First the momentum and position operators are defined in terms of "...
321 views

### Physical intuition/interpretation of fractional derivatives/integrals?

Oftentimes, when the derivative and integral operations are introduced within the realm of physics, we are taught some physical interpretation of them: Velocity is the derivative of position ...
732 views

### A confusion from Weinberg's QFT text (a vanishing term in Lippmann-Schwinger equation)

I was reviewing the first few chapters of Weinberg Vol I and found a hole in my understanding in page 112, where he tried to show in the asymptotic past $t=−∞$, the in states coincide with a free ...
323 views

### Why is the $dx$ right next to the integral sign in QFT literature?

I've noticed that in QFT literature, integrals are usually written as $\int \!dx ~f(x)$ instead of $\int f(x) dx$. Why?
636 views

599 views

### A basic math identity often used in integrals [closed]

I'm just wondering about why $y_i=A_{ij}x_j$ implies $$d^Ny=|\det A|d^Nx.$$ I see that $\det A$ is the product of the eigenvalues of a diagonal matrix but still don't exactly see how. Please help.
528 views

### Physical significance of getting an non-integrable function in an equation

I just found out during my Calculus course in High School, that there exist functions which cannot be integrated. Then I thought that I come across a lot of integrals while solving Physics questions....
119 views

2k views

### Getting position from an accelerometer on an Android phone

I know that integrating acceleration twice will give me position (acceleration-->velocity-->position) but how can I do all this when I all I have are a set of data points (ex: 1 second = some # m/s^2);...
74 views

### What's the probability distribution of a deterministic signal or how to marginalize dynamical systems?

In many signal processing calculations, the (prior) probability distribution of the theoretical signal (not the signal + noise) is required. In random signal theory, this distribution is typically a ...
595 views

### Does the universe obey the holographic principle due to Stokes' theorem?

Does the universe obey the holographic principle due to Stokes' theorem? $$\int\limits_{\partial\Omega}\omega = \int\limits_{\Omega}\mathrm{d}\omega.$$ Can this ...
1k views

### Newton's original proof of gravitation for non-point-mass objects

Suppose we have two bodies, one very large (Earth), and one very small (a cannon ball). If the cannon ball is some distance away from the Earth, to find out the force produced on the cannot ball, we ...
342 views

### Extension to continuous in proofs of rigid body mechanics

I'm studying rigid body mechanics and I've seen several proofs of properties related to total angular momentum, kinetic energy, etc. that all regard discrete set of points. For example, to show that ...