# Questions tagged [mathematics]

DO NOT USE THIS TAG just because your question involves math! If your question is on simplification of a mathematical expression, please ask it at math.stackexchange.com The mathematics tag covers non-applied pure mathematical disciplines that are traditionally not part of the mathematical physics curriculum, such as, e.g., number theory, category theory, algebraic geometry, general topology, algebraic topology, etc.

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26 views

### Correlation among the terms “convergence”, “accumulation” and “explosion”

I am developing an essay on music perception by approaching some mathematical and physical notions. As such, the term I am addressing and interested in is the "convergence", which pairs in mathematics ...
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### What is the most important thing to master in string theory? [closed]

What is the most important material to MASTER in string theory? I am asking this question because there are thousands of people working on string theory and it is really hard to get a job in this ...
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### How to calculate the total gravitational potential energy of a vertical object (do we use integration?)

Hello I was reading another question asked by zach466920, and when he was trying to calculate the total GPE of a water 'tower', he used this explanation: He basically used integration to calculate ...
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### What is the syntax in scilab to derivative a function like $x/log(x)$, not a polynomial? [closed]

In scilab to do a derivative I used the syntax derivative as: Function y=f(x) y=x/log(x) endfunction disp(derivative ("f","x",4)) And my output was: Undefined variable: derivative Where was I ...
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### Is the derivative of $2e^3$ is $2e^3$ if not then why because $e^3$ is also of the form $e^x$? [closed]

I have only the knowledge of basic mathematics.
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### Does the concept of infinity have any relevancy or application in Physics and applied Physics? [duplicate]

Does the concept of infinity have any relevancy or application in Physics and applied Physics? I must admit that I am not particularly knowledgeable in the area of Physics, but I have never seen the ...
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### Solution of DE regarding SHM, kinda

Firstly, let me explain the situation So this year in my core module, modern physics, all of our practicals are simulations of general stuff programmed in SageMath/Jupyter Notebook. We are still in ...
1k views

### Are there undecidable statements in classical mechanics?

Do Gödel's incompleteness theorems have any significance or application to axiomatic theories of classical mechanics like Newton's for example?
2k views

### Which mathematical property allows us to combine proportional relationships?

Coulumb's law states that $$F \propto q_1 \cdot q_2 \tag{1}$$ and $$F \propto \frac{1}{r^2} \tag{2}$$ Why can we combine these two proportions into $$F \propto \frac{q_1.q_2}{r^2}?$$ What ...
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### Does Weyl's tile argument defeat the discrete spacetime?

Weyl shows that in a discrete spacetime Pythagoras's theorem fails to arise. Of course it may be that although Pythagoras's theorem arises naturally but actually does not model the real world. So Does ...
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### Classification of higher Symmetry Protected Topological (SPT) phases

Suppose that we have a $d$ dimensional bosonic SPT phase, protected by some $p$-form symmetry, $G^{[p]}$. Suppose also that it is classified within group cohomology, so that we don't have to run into ...
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### Are there cases where the use of the Grassmann variables simplifies computations in the usual bosonic analysis?

When one introduces complex numbers and complex analysis one can then use the new machinery to solve some real-analysis problems. A lamppost example is computing integrals via residues. I think I've ...
8k views

### Can a mathematical proof replace experimentation?

I know that this is very similar to How important is mathematical proof in physics? as well as Is physics rigorous in the mathematical sense? and The Role of Rigor. However, none of the answers to ...
294 views

### Are all representations of a finite group unitary?

I am reading Zee's Group theory in a nutshell for physicists and came across the following theorem (Page 96): Unitary representations The all-important unitarity theorem states that finite ...
99 views

### Is Snell’s Law valid in this case?

When light travels in a perpendicular path from one medium to another medium of different optical density, is Snell’s law valid? $\sin i$ and $\sin r$ are both 0, right? So it isn’t valid. Is this ...
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### Integration and average in physics? [closed]

Many applications of physics theory involve computations of integrals. Examples are voltage, force due to liquid pressure, surfaces... In some cases, when there is linear dependence between two ...
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### Why are galilean transforms affine? [duplicate]

Here is a decomposition of galilean transforms of the form $x\mapsto Ax+y.$ Why are they all of this form? $T$ galilean is distance preserving so it is also injective. Take $B_r(a)$ the closed $r-$...
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### Higher dimensional version of Stoke's Theorem / Divergence theorem

I've learnt about Stokes' Theorem and the divergence theorem that relate integrals of functions over manifolds to integrals of related functions around the boundary of the manifolds but all in 3-...
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### Bessel function of first kind [closed]

Can someone tell me how $$\frac{1}{T}\int_0^T e^{i(m-n)\omega t} e^{-ix\sin(\omega t)} e^{iy\sin(\omega t +\phi)}\, dt = J_{m-n}\left(\sqrt{x^2 +y^2 -2xy\cos(\phi)}\right)?$$
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### Quantum Mechanics Spectral theorem proof [closed]

Has anyone an idea how to prove the spectral theorem $A = \sum_{i} \lambda_i P_{\lambda_{i}}$. Starting from $A|\Psi_{i}\rangle=\lambda_{i}|\Psi_{i}\rangle$ or what ever?
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### Groups with cardinality larger than the Reals in physics

In what physical theories are sets with cardinality larger than $\aleph_1$ used? There are plenty of examples of finite, countable, and uncountable vector spaces in physics, but do physicists ever ...
86 views

### Does incomplete differentials $\delta Q$ or $\delta W$ have potentials? [closed]

I am very confused because my text book have following formula. $$dU = \delta Q \tag {1-1}$$ $$dU = \delta W \tag {1-1'}$$ Because these might mathematically mean "incomplete derivative = ...
103 views