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 ...

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0answers
29 views

Is it possible to express continuous growth without using transcendental numbers?

Continuous growth is typically expressed using some variant on $A = Pe^{rt}$, I understand where $e$ comes from in general, it is the amount something grows in a given time interval, when continuously ...
0
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0answers
9 views

Atomic flux on the surface?

I have a surface which is made up of two triangles of unequal areas. I impinge a single atom on the surface at a certain angle at a certain time interval. As flux is atoms/unit area/unit time. In ...
3
votes
1answer
75 views

What really are perturbation expansions?

I'm unsure if this question belongs here or at Math.SE, but since I've got to it by reading some articles about Physics I'm going to post it here anyway. In this particular article (Theoretical ...
0
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1answer
24 views

Calculating average quantities in kinetic theory

Consider a volume $V$ with $5$ particles each of mass $m$ at positions $\mathbf{q}_i=(x_i,y_i,z_i) \in V$ and with velocities $\mathbf{v}_i=(u_i,v_i,w_i)$. The speeds of the particles are between $0$ ...
0
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0answers
35 views

The concept of continuity in a topological group [migrated]

I am now learning the Lie group theory. People talk about the fundamental group of a topological group. The problem is, how is the continuity defined in a topological group? In other words, in which ...
0
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0answers
29 views

Nonlinear matrix differential equation [migrated]

I am working with the following differential equation: $$\dot{x_i} = \sum_j A_{ij} x_j + x_i \sum_j B_{ij}x_j$$ which is essentially in matrix notation: $$\dot{\mathbf{x}} = A\mathbf{x} + ...
1
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0answers
7 views

Real numbers and rationals - Decimal Expansion [migrated]

How would one endeavor to show that A real number is rational if and only if its decimal expression ends in recurring digits?
1
vote
1answer
46 views

The grand partition function of non interacting hamiltonians

In the case of non interacting particles I know we can write the Hamiltonian as $$H(\mathbf{q}_1,\dots,\mathbf{p}_1,\dots)=\sum_{i=1}^N h(\mathbf{q}_i,\mathbf{p}_i)$$ but I am having trouble ...
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0answers
9 views

Poisson bracket in 4d phase space

In phase space determined by $(q_i,p_i)$ the Poisson bracket of two functions f and g is $$\{f,g\}=\sum_{i=1}^N\frac{\partial f}{\partial q_i}\frac{\partial g}{\partial p_i}-\frac{\partial g}{\partial ...
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votes
0answers
11 views

Find multiple integral equation solution [migrated]

$\int_{\theta=0}^{\pi}\int_{\phi=0}^{2\pi}((v\cos\theta\sin\phi+v')^2+(v\sin\theta\sin\phi)^2+(v\cos\phi)^2)\rho r^2\sin\theta d\theta d\phi$ Can you solve this equation please I use symbolab but I ...
5
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5answers
376 views

Infinite series of derivatives of position when starting from rest

Suppose you have an object with zero for the value of all the derivatives of position. In order to get the object moving you would need to increase the value of the velocity from zero to some finite ...
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0answers
36 views

Langrange multiplier

What does it mean in Langrange multiplier in one interpretation when in example occurs minimum potential that is given by roote from two/two why must be this value given in this mode? It can be in ...
1
vote
2answers
180 views

Number of microstates compatible with two boxes

From my notes I have: From one point of view there are many more microstates compatible with the LHS than the RHS, in fact the relation between the number of microstates is ...
2
votes
1answer
232 views

Resources for theory of distributions (generalized functions) for physicists

I am looking for tutorials, articles or books containing theory of distributions in context of mathematical physics. Please suggest.
3
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4answers
3k views

How many digits of Pi are required in physics? [closed]

In other words: which physics experiment requires to know Pi with the highest precision?
2
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2answers
55 views

Can I take the partial derivative of the Lagrangian with respect to a constant?

I've got a system where I know that the derivative of one of the generalized coordinates is constant. So to find the Hamiltonian of the system I need to take the partial derivative with respect to ...
3
votes
1answer
273 views

Why are three parameters required to express rotation in 3 dimension?

We know that in spherical coordinates angle $\theta$ and $\phi$ (two angles)are enough to express three dimensional rotation of matrix. But to express rotation mathematically as a transformation ...
55
votes
14answers
15k views

Best books for mathematical background?

What are the best textbooks to read for the mathematical background you need for modern physics, such as, string theory? Some subjects off the top of my head that probably need covering: ...
20
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7answers
1k views

Tensor Operators

Motivation. I was recently reviewing the section 3.10 in Sakurai's quantum mechanics in which he discusses tensor operators, and I was left desiring a more mathematically general/precise discussion. ...
1
vote
1answer
50 views

Every Galilean transformation can be written as the composition of rotation, translation, and uniform motion

Having heard many good things about Arnold's Mathematical Methods of Classical Mechanics, I picked it up and started going through it. While I think I understand all of the definitions he makes, the ...
1
vote
1answer
44 views

Description of charged sphere with Heaviside function in cylindrical coordinates

I need to describe density of charge of uniformly charged sphere (radius R, total charge Q, position of centre (0,0,0)) with Dirac delta function and Heaviside step function. The hard part is to ...
3
votes
2answers
438 views

Hilbert's sixth problem (current answers neglect the fact that $C_{U} \subseteq U $ ) [duplicate]

(current answers neglect the fact that the set of all concepts( $C_{U}$) is a subset of U as all of them are physically encoded( symbolically represented by the physical events themselves(brains, ...
2
votes
3answers
701 views

Mathematics for Quantum Mechanics [duplicate]

What math should I study if I want to get a basic understanding of quantum mechanics and especially to be able to use the Schrodinger's equation.
0
votes
1answer
54 views

Requirements prior to Quantum Mechanics [duplicate]

What are the requirements in physics and mathematics that somebody must have in order to start learning Quantum Mechanics by himself?
5
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4answers
977 views

Intuitive meaning of the exponential form of an unitary operator in Quantum Mechanics

I'm an undergraduate student in Chemistry currently studying quantum mechanics and I have a problem with unitary transformations. Here in my book, it is stated that Every unitary operator ...
2
votes
4answers
72 views

Dual of the TDSE

Quite a quick and hopefully simple question. The TDSE takes the form $$i\hbar\frac{\partial\lvert\psi\rangle}{\partial t}=H\lvert\psi\rangle$$ and so if we take the dual of this to find the time ...
13
votes
2answers
1k views

Can quaternion math be used to model spacetime?

Quaternions are commonly used to model 4 dimensional systems where the quaternion consists of a real 3 dimensional vector and an imaginary scalar. So on the surface Quaternions seem well suited to ...
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0answers
51 views

Justifying the use of real numbers for measuring length

I am not sure if this is the most appropriate place to post this but here goes nothing: Assume we were trying to come up with system of numbers $S$ to model our intuition of length. We want $S$ to ...
4
votes
1answer
100 views

Which cardinality of infinities are subtracted in the renormalisation of quantum field theory?

In quantum field theory, e.g. in quantum electrodynamics, renormalisation is used to make sense of an infinite number of virtual particles. This, crudely, involves the subtraction of infinities. But ...
4
votes
10answers
2k views

Is it possible for a physical object to have a irrational length?

Suppose I have a caliper that is infinitely precise. Also suppose that this caliper returns not a number, but rather whether the precise length is rational or irrational. If I were to use this ...
0
votes
0answers
35 views

Gauge invariance and non-commuting second derivatives

I'm currently doing a homework assignment in relativistic quantum mechanics, and one of the problems involves proving the gauge invariance of a particular lagrangian. The problem is really quite ...
0
votes
2answers
59 views

Calculating the electric field of an infinite flat 2D sheet of charge

I was trying to calculate the electric field of an infinite flat sheet of charge. I considered the sheet to be the plane $z=0$ and the position where the electric field is calculated to be ...
0
votes
1answer
61 views

What is the relationship between completeness of wave functions and completeness of Hilbert space?

In the lecture, my prof said that completeness means that any wave function can be constructed using an infinite number of "other" basis wave functions. This is very intuitive since this is nothing ...
0
votes
0answers
37 views

Solving inhomogeneous Stokes equation

I want to solve the Stokes inhomogeneous equation, i.e. $$\nabla^2 \vec v -\nabla P = \vec f(r,\theta)$$ $$\nabla\cdot\vec v=0$$ where $\vec f$ is irrotational, i.e. $\partial_y f_x - \partial_x ...
0
votes
1answer
43 views

Role of math in science [closed]

Is it important for a physicist to be good at math? Should he be on par with a mathematician? According to me physics and math are like English and biology we study them in the same language but they ...
0
votes
0answers
46 views

Algebraic number theory and physics [duplicate]

I would like to ask if there are any aspects of algebraic number theory related to physics (for example in string theory or Moonshine etc). I am thinking of attending a course on algebraic number ...
0
votes
2answers
125 views

Significance of $\pi$ in physics

We all know this magical mathematical constant. My question being , how and why pi just shows up in every other physics derivation or formula or even statistics for that matter . ...
0
votes
2answers
109 views

Study material for quantum mechanics [duplicate]

I want to study quantum mechanics. But I don't know what and which topics of mathematics are required. I know a bit of differential calculus. But what else is needed to study a bit advanced quantum ...
0
votes
0answers
54 views

Good book for learning about mathematical foundation of quantum physics [duplicate]

I've been trying to slog through Quantum Physics for Dummies, but can't even get past the first chapter. There's a lot of talk of Bras, Kets, and Hilbert spaces, but I feel I'm missing the ...
0
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0answers
42 views

Simple math used for physics

I read the book "Analysis 1" by Harro Heuser about calculus and it several interesting chapters about applications of mathematics for physics. For example there was one part of the chapter, which ...
2
votes
0answers
97 views

The implications of Gödel's Second Incompleteness Theorem on Theoretical Physics models

Does Gödel's Second Incompleteness Theorem imply that no Theoretical Physics model of reality can be proved to be consistent using the laws of physics? I work partially in Quantum Information Theory ...
0
votes
0answers
31 views

Quantum mechanics and distribution law in mathematical logics

Recently I've heard that quantum mechanics can be formulated by starting from the rejection of distribution law in mathematical logic: $a$ and $(b$ or $c)$= $(a$ and $b)$ or $(a$ and $c)$. Did ...
7
votes
7answers
2k views

Why are radians more natural than any other angle unit?

I'm convinced that radians are, at the very least, the most convenient unit for angles in mathematics and physics. In addition to this I suspect that they are the most fundamentally natural unit for ...
4
votes
2answers
207 views

In what way are the Mathematical universe hypothesis and A New Kind of Science connected

The Mathematical universe hypothesis, mainly by Max Tegmark and A new Kind of Science, mainly by Stephen Wolfram both claim (as least as I understand it) that at its innermost core reality is ...
27
votes
8answers
4k views

Classical mechanics without coordinates book

I am a graduate student in mathematics who would like to learn some classical mechanics. However, there is one caveat: I am not interested in the standard coordinate approach. I can't help but think ...
5
votes
4answers
291 views

Kähler and complex manifolds

I was wondering if anyone knows any good references concerning Kähler manifolds and complex manifolds? I am studying supergravity theories and for the simplest $\mathcal{N}=1$ supergravity we will get ...
1
vote
2answers
83 views

A question over the reality of $\sin x$

Harmonic functions are in widespread use in physical descriptions of natural real phenomena. I am just wondering therefore how we can define $\sin(x)$ to be part of a real physical quantity (with ...
0
votes
1answer
54 views

Do logarithms appear inside the divergent UV integrals? If so why? [closed]

Do logarithms appear inside the UV divergent integrals of $q\cdot f\cdot t$? I mean expressions of the form of $ \int_{V}d^{r}f(p)log(p^{2}+m^{2}) $ In this case, can we approximate it by $ log(p)= ...
1
vote
1answer
142 views

What kind of math is used in QFT? [duplicate]

What branch(es) of math are used in Quantum Field Theory? Or the question, by way of analogy: Tensor Calculus is to General Relativity as What is to Quantum Field Theory?
15
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2answers
7k views

How is the Saddle point approximation used in physics?

I am trying to understand the saddle point approximation and apply it to a problem I have but the treatments I have seen online are all very mathematical and are not giving me a good qualitative ...