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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15
votes
4answers
2k views

What is the physical meaning of a “complete” Hilbert space in QM?

What does the word "complete" means from the physical point of view? I do not understand what it physically means to say that a Hilbert space is a complete vector space.
6
votes
6answers
3k views

How is gradient the maximum rate of change of a function?

Recently I read a book which described about gradient. It says $${\rm d}T~=~ \nabla T \cdot {\rm d}{\bf r},$$ and suddenly they concluded that $\nabla T$ is the maximum rate of change of $f(T)$ ...
0
votes
1answer
277 views

How to describe the inner curve of a crescent?

What is the equation which describes the inner circle of the crescent that a celestial body displays when view at an angle from its light source, as a function of the crescent-cycle period? For ...
31
votes
10answers
2k views

Readable books on advanced topics [closed]

I realise that there are already a few questions looking for general book recommendations, but the motivation and type of book I'm looking for here is a little different, so I hope you can indulge me. ...
3
votes
3answers
3k views

Why is the angle of a pendulum as a function of time a sine wave?

OK so I'm trying to understand why the angle of a pendulum as a function of time is a sine wave. I can't really find an explanation online and when I do find something partial there are certain ...
11
votes
3answers
1k views

Mathematical Physics Book Recommendation [duplicate]

Possible Duplicate: Best books for mathematical background? I want to learn contemporary mathematical physics, so that, for example, I can read Witten's latest paper without checking other ...
4
votes
2answers
482 views

Why model space with real numbers?

Are there any good papers discussing why we use $\mathbb{R}^{3}$as a model for space? More specifically are there any that explain why we don't use other number systems such as extensions of the real ...
33
votes
10answers
1k views

Examples of number theory showing up in physics

My question is very simple: Are there any interesting examples of number theory showing up unexpectedly in physics? This probably sounds like rather strange question, or rather like one of the ...
3
votes
2answers
164 views

Infinitesimal input, macroscopic output

I must admit that I never got well how physicists handle infinitesimal quantities, mainly because of my education as a mathematician. So the following lines (taken from the preface of Berezin and ...
2
votes
3answers
876 views

What does the differential of $d_s\sin(\theta) = m\lambda$ help us see, with respect to waves through diffraction gratings?

With respect to waves traveling through a diffraction grating, we have an equation like this one: $$d_s\sin(\theta) = m\lambda.$$ Where $d_s$ is the distance between slits in the grating, $\theta$ is ...
3
votes
2answers
480 views

What are some interesting calculus of variation problems? [closed]

That I could create as a classical mechanics class project? Other than the classical examples that we see in textbooks (catenary, brachistochrone, Fermat, etc..)
2
votes
1answer
107 views

Causality and operationalism: from sets and functions to monads

When working in a laboratory, the most basic behaviour is to turn a knob or dial and then see a transformation of some data output. An example is increasing a magnetic field and seeing Zeeman ...
0
votes
3answers
1k views

Sine wave, $\pi$ and frequency

Please explain the relation $\sin(2\pi ft)$ such that how the $\pi$ (which is actually circumference/diameter of a circle) relates with the sine wave which is having a longitudinal vibration?
1
vote
0answers
73 views

Reference request: Introductions to current mathematics derived from / related to gauge theories (in physics) [duplicate]

I was searching for introductions to current mathematics derived from / related to gauge theories in physics. Can someone suggest some good references? E.g. Topics in Physical Mathematics by K. ...
3
votes
2answers
202 views

An integral related to QFT

How to show $$\displaystyle\int\int\int f(p,p')e^{ip\cdot x-ip'\cdot x}d^3pd^3p'd^3x=(2\pi)^3\int f(p,p)d^3p$$ ? I have $p\cdot x=Et-\bf p\cdot x$
1
vote
2answers
1k views

What is the physical meaning of a product of vectors?

My teacher told me that Vectors are quantities that behave like Displacements. Seen this way, the triangle law of vector addition simply means that to reach point C from point A, going from A to B ...
13
votes
5answers
23k views

What is the math knowledge necessary for starting Quantum Mechanics?

Could someone experienced in the field tell me what the minimal math knowledge one must obtain in order to grasp the introductory Quantum Mechanics book/course? I do have math knowledge but I must ...
0
votes
0answers
93 views

Literature request for books / review papers on gravitation, gauge theories and related mathematics [duplicate]

Similar to this reference, are there more such references / works [including textbooks] available in the literature? (A list would be greatly welcomed and appreciated.) With great appreciation.
4
votes
7answers
991 views

For a theoretical (not mathematical) physicist, is there a need to learn pure mathematics?

For a theoretical physicist (not a mathematical physicist), is there a need to learn pure mathematics ?
3
votes
2answers
544 views

What is the mathematical formulation for buckling?

Argument: Buckling is an engineering concept that can only be applied to thin columns with compressive loading. (Is it possible to) Prove the above sentence right or wrong with mathematical ...
2
votes
1answer
201 views

What determine whether the dynamical equations are tensor equations or vector equations?

Newton's 2nd law which is central to Newtonian dynamics, is a vector equation $\sum\textbf{F}_{external}=m\textbf{a}$ Same with Maxwell's equations in the covariant form. On the other hand, ...
5
votes
3answers
2k views

What is a antiunitary operator?

In field theory one can define a time reversal operator T such that $T^{-1} \phi (x) T = \phi (\mathcal T x)$. It is then proved that T must be antiunitary: $T^{-1} i T = -i$. How is this equation ...
11
votes
8answers
802 views

Mathematical Universe Hypothesis

What is the current "consensus" on Max Tegmark's Mathematical Universe Hypothesis (MUH) which claims every concievable mathematical structure exists, including infinite different Universes etc. I ...
50
votes
11answers
9k views

Quantum Field Theory from a mathematical point of view

I'm a student of mathematics with not much background in physics. I'm interested in learning Quantum field theory from a mathematical point of view. Are there any good books or other reference ...
12
votes
1answer
416 views

Covariant derivatives

I need correctly define covariant derivatives on the coset space $G/H$, where a group $G \equiv \{X_i, Y_a\}$ ($X$ and $Y$ are generators) have a subrgroup $H \equiv \{X_i\}$ Lie algebra of $G$ has ...
3
votes
1answer
358 views

Is there a mathematical way to describe how a flame flickers?

I love the way candles flicker. It's a great effect and I almost want to see it replicated in an actual lightbulb. I was curious if there is any way to express that mathematically? I'm not that ...
64
votes
6answers
3k views

The Role of Rigor

The purpose of this question is to ask about the role of mathematical rigor in physics. In order to formulate a question that can be answered, and not just discussed, I divided this large issue into ...
37
votes
8answers
4k views

Does Gödel preclude a workable ToE?

Gödel's incompleteness theorem prevents a universal axiomatic system for math. Is there any reason to believe that it also prevents a theory of everything for physics? Edit: I haven't before seen ...
3
votes
2answers
3k views

Calculating uncertainty in the final result (combining uncertainties)

I'm struggling to determine the uncertainty in $F$ so it would match the textbook answer. The problem statement is: A force F is obtained using the equation: $F = \frac{mv^2}{2\pi(x_2 - x_1)}$. The ...
0
votes
1answer
699 views

Reference area of a parachute

I am trying to do an aerodynamic drag equation on a descending parachute (the round variety) and have no idea what the reference area on one would be. I know for a sphere, you can use radius*radius*PI ...
16
votes
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 ...
9
votes
2answers
534 views

Transforming a sum into an integral

I posted this in the mathematical forums. Maybe you will help me. I found an hard article http://prola.aps.org/abstract/PR/v105/i3/p776_1 of yang huang and luttinger. The authors begins with the sum: ...
3
votes
4answers
666 views

Generalized functions in physics

Prior to the Dirac delta function, what other distributions functions where physicists using? I find it hard to motivate the theory of generalized functions with just the delta function alone.
0
votes
1answer
478 views

Functional Derivative of Convolution

How to carry out the following functional derivative? $$\frac{\delta F}{\delta n(r)}$$ where $$F=\int dr n(r) \int C(|r-r'|) n(r') dr'$$ is it simply: $$2 \int dr' C(|r-r'|) ...
18
votes
5answers
15k views

How can area be a vector?

My professor told me recently that Area is a vector. A Google search gave me the following definition for a vector: Noun: A quantity having direction as well as magnitude, esp. as determining ...
2
votes
1answer
78 views

What interpretive difference is there between defining a function with or without a differential as a postfactor?

I have thought about this and looked for answers for a long time now, but I do not have any name or label for this problem, which is the reason for the long title of this question. I have come across ...
2
votes
7answers
353 views

Book request for an abstract treatment of QM without using any particle formalism

I am an electronics and communication engineer, specializing in signal processing. I have some touch with the mathematics concerning communication systems and also with signal processing. I want to ...
4
votes
2answers
294 views

Combinatorial sum in a problem with a Fermi gas

I'm solving a problem involving a Fermi gas. There is a specific sum I cannot figure my way around. A set of equidistant levels, indexed by $m=0,1,2 \ldots$, is populated by spinless fermions with ...
25
votes
11answers
10k views

What is the logarithm of a kilometer? Is it a dimensionless number?

In log-plots a quantity is plotted on a logarithmic scale. This got me thinking about what the logarithm of a unit actually is. Suppose I have something with length $L = 1 km$. $\lg L = \lg km$ It ...
14
votes
7answers
2k views

The philosophy behind the mathematics of quantum mechanics

My field of study is computer science, and I recently had some readings on quantum physics and computation. This is surely a basic question for the physics researcher, but the answer helps me a lot ...
2
votes
4answers
300 views

Can we make a change of variables (for example to polar coordinates) into a divergent integral?

I know that if the integral is convergent we can always make a change of variable to make it better, however what happens with DIVERGENT integrals? can we make a change of variable into a divergent ...
6
votes
1answer
615 views

Is C60 really the “most spherical” fullerene?

In the late 80's and early 90's, Smalley and others made claims that the C60 fullerene bearing icosahedral symmetry was the most spherical molecule known, and perhaps the most spherical that could ...
2
votes
6answers
3k views

real world applications of Mathematics which use functions with singularities, not just as a matter of mathematical taste but for conceptual reasons

EDIT [for aptness of this question to this site, read 'real world applications' as 'applications in Physics'] The concept of function (of the form $f : \mathbb{R} \to \mathbb{R}$ ) has been used in ...
8
votes
6answers
504 views

Objects in Physics as a mathematician would see them

I'm a mathematician with hardly any knowledge of physics. Before I start reading volumes of physics books, I have a few questions that have been bugging me and that will help me start reading physics. ...
11
votes
1answer
16k views

Where does this equation originate from? (found in the Big Bang Theory)

Recently, I've been watching "The Big Bang Theory" again and as some of you might know, it's a series with a lot of scientific jokes in it - mostly about Physics or Mathematics. I understand most of ...
-1
votes
1answer
887 views

How to simplify e to power of j.t [closed]

I have exam tommorow and cant get this figured out :( dont blame me but please answer this question. I Want to simplify this term: 3 times ((e topowerof 5jt) + (e topowerof -5jt)) Thanks.
2
votes
2answers
518 views

How do you find conserved quantities for linear second order ODEs?

I have a differential equation of the form $ \frac{d^2 y}{dt^2} + f(t) \frac{dy}{dt} + g(t) y = 0 $ where $f$ and $g$ are known functions of time. Is there a systematic (or otherwise) way of ...
2
votes
2answers
292 views

a question on Lagrange's equation when the time derivative of the generalized co-ordinates is constant

Consider a system whose generalized co-ordinates are $q_i$ and is under the constraints $\dot{q_i} = K_i \forall i = 1,2,3,...$ where $K_i$ are constants. I have a problem in writing the Lagrange's ...
10
votes
3answers
568 views

infinite grid of planets with newtonian gravity

Assuming only Newtonian gravity, suppose that the universe consists of an infinite number of uniform planets, uniformly distributed in a two-dimensional grid infinite in both directions and not moving ...
2
votes
2answers
735 views

Helmholtz decomposition in the plane

Prove or disprove the following proposition: For any smooth plane vector field $\mathbf{H}=\left(H_x,H_y\right)$, there exist scalar potentials $\phi$, $\psi$ such that $H_x=\frac{\partial \phi ...