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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2
votes
1answer
74 views

Cancelling the partial of a coordinate, $\partial q$, with the element of a coordinate, $dq$ in Physics [closed]

I've seen in many books, things like this ( I will be simple ): $$\int \frac{\partial f}{\partial q} dq=\int df$$ where $f$ is a function of $q$ and other coordinates. I just axiomatically assumed ...
2
votes
2answers
158 views

Why is $\pi$ the value it is? [closed]

Why is the value of $\pi$ 3.141592...(etc.)? Is it a fundamental property of our universe? Or does it follow from our definition of what a circle is, or does it otherwise follow from the way we ...
2
votes
3answers
117 views

Why does Griffiths define the complex inner product differently? [closed]

I have just now noticed that Griffiths (in his book Introduction to Quantum Mechanics) defines the complex inner product as $\big<z,w\big>=\sum_{i=1}^n\overline{z}_iw_i$. In all mathematics ...
1
vote
0answers
41 views

Given a dimension of a known object in the image, how can we calculate the dimension of other objects in the same image ?

The question considers a very specific scenario in which we have an image with let us say, two rectangle objects. We know width and height of one object. How can we calculate the dimensions of the ...
0
votes
1answer
73 views

Causality and response functions

Referring to David Tong's notes on Electromagnetism, page 29 (of the PDF, numbered 183), section 7.5.4; It is proved that the frequency domain response function (in this case describing the ...
1
vote
2answers
102 views

See the opposite wall on a mirror [closed]

I'm in tenth standard. This is a higher-order-thinking-skills Q I found in a book. One is supposed to use laws of reflection ($\angle i = \angle r$). You can also use mathematical concepts like ...
1
vote
0answers
31 views

Mathieu equation and instabilities

Consider the Mathieu equation $$ \tag 1 y'' + (A -2q\cos(2t))y = 0, $$ How does it provide instabilities for small $q << 1, A > q$? I don't understand this because as the result of ...
1
vote
1answer
134 views

Book on gamma functions with applications in physics

I have heard that in my next semester, our quantum mechanics teacher will be giving a great emphasis on difficult integrals with the most of them having to do with gamma functions. Does anybody know ...
2
votes
2answers
220 views

Can all of physics be described by simple math? [closed]

Recently I was browsing through A Dynamical Theory of electromagnetic field by Maxwell and wondered because the paper did not seem to include any vector calculus or any vectors. I thought of the ...
1
vote
0answers
36 views

Mathematics involved in string theory [duplicate]

As an amateur mathematician and lover of the sciences I have a well working knowledge of classical mechanics, quantum mechanics, general relativity, quantization, and so on... But recently I've been ...
2
votes
1answer
120 views

How to prove that sum converges to integral using density of states?

Essentially, I would like to prove $$ \sum_k f(k) \to \int f(k) \rho dE \tag{1}$$ where $$ \rho = \frac{dk}{dE} \tag{2}$$ is the density of states and $k \to \infty$. The model is that there is a ...
1
vote
0answers
83 views

Any other mathematical fields in physics than $\mathbb{R}$ or $\mathbb{C}$? [closed]

In physics, we usually use the real number field $\mathbb{R}$ or the complex number field $\mathbb{C}$. Does any other field find use in physics too?
1
vote
2answers
136 views

Reference for mathematics of statistical mechanics

I'm looking for materials (books, articles, etc) which focus ONLY on the mathematics of statistical mechanics (as I have no background in physics). The materials may have some simple explanations or ...
2
votes
1answer
129 views

Why Newton wanted lines to be generated by continued motion of points rather than by apposition of parts?

The following passage has been extracted from the Newton's (John Stewart's English translated version) "Sir Issac Newton's two Treatises: Of the Quadrature of Curves, and Analysis by equations of an ...
1
vote
1answer
31 views

Formula relating sum of values of a function to its integral

I came across the above formula in some quantum mechanics lecture notes explaining the Casimir effect. Anyone seen it before if so could you please tell me its 'name'. B refers to the Bernoulli ...
13
votes
5answers
931 views

What does it mean for a physical quantity if its mixed second partial derivatives are not equal?

This goes for every problem (either in electromagnetism or fluid dynamics) that has to do with vector fields. Say we have a fluid flowing in a closed circular pipe (or an electromagnetic field, the ...
4
votes
2answers
56 views

Pointwise and uniform convergence. Examples from physics

I am a first-year mathematical student, and from a mathematical perspective I understand the difference between pointwise and uniform convergence of sequences and series of functions. However, I have ...
-2
votes
0answers
48 views

Subject is Maths that would complement Physics? [closed]

Suppose Math has 5 sub parts- Analysis: Analysis, Complex Analysis, Measure theory and integration,Functional Analysis Algebra: Group Theory, Vectors space-rings-modules, Galois, Algebra Number ...
2
votes
2answers
251 views

Mathematics needed for string theory [duplicate]

I'm interested in cutting edge string theory studied by research physicist. I'm wonder what mathematics is needed and how far am I in terms of mathematics background needed and how much more ...
-4
votes
3answers
145 views

Can pure mathematics alone give proofs in science [closed]

I reasoned in my last post that because of science's nature of induction and falsifiability, it is impossible to give a theorem in science, unlike in mathematics. It is because even when a scientific ...
1
vote
1answer
85 views

Numerically summing a divergent series [duplicate]

Say I have a closed form expression for a divergent series and I can calculate as many terms in it as I want. What options have I got to obtain a meaningful result for this divergent series?
1
vote
1answer
117 views

Trajectories piecewise smooth?

In my studies of calculus and real analysis I have found the proofs of several theorems, commonly used in physics, such as those concerning the conservativity of fields, for example like If ...
1
vote
0answers
42 views

Dirac delta function equation intuition and proof [duplicate]

What is the intuition and where should I find proof of this equation (do not know what its name is). It is used to derive Gauss law from Newton equation. $${\nabla \cdot \Bigg ( ...
6
votes
5answers
785 views

Is it possible to have infinite combinations in reality?

On a yoghurt advert, the voiceover claimed that you have infinite combinations with it. However, given that there is a finite amount of matter, is it possible to have infinite combinations with the ...
2
votes
0answers
101 views

Convert discrete sum to principal integral

I'm studying IQHE beginning with Laughlin's famous gauge argument. I referred to his Nobel Lecture, in which he mentioned a paper that enlightened him. It is Phys.Rev.B.23.5632(1981) which talked ...
1
vote
0answers
67 views

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

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 ...
3
votes
1answer
89 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 ...
1
vote
1answer
63 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 $0$ ...
1
vote
1answer
93 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 ...
1
vote
2answers
219 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
2answers
105 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 ...
5
votes
1answer
367 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 ...
1
vote
1answer
261 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 ...
2
votes
1answer
164 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 ...
1
vote
1answer
100 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?
2
votes
4answers
91 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 ...
15
votes
3answers
2k 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 ...
1
vote
0answers
84 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
116 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 ...
1
vote
0answers
55 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 ...
1
vote
2answers
95 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 ...
1
vote
1answer
198 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 ...
1
vote
0answers
59 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 ...
1
vote
1answer
52 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 ...
1
vote
0answers
80 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 ...
3
votes
2answers
496 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, ...
0
votes
2answers
252 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 . ...
1
vote
2answers
157 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 ...
1
vote
0answers
61 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 ...
1
vote
0answers
56 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 ...