Theorem Definition and 1000 Threads

In Grosso's Solid State Physics, chapter 1, page 2, The author said that: Therefore, I plug (4) into (1), and I expect that I can get the following relationship, which proves that ##H\left|W_{k}(x)\right\rangle## belongs to the subspace ##\mathbf{S}_{k}## of plane waves of wavenumbers...

Hello all, I have only seen this paper brought up here once before based on the search function 2 years ago, and the thread devolved into something off topic within the first page. I am asking in reference to this paper: https://arxiv.org/pdf/1604.07422.pdf Which claims to show that single...

What exactly does the statement of poynting theorem mean physically?

I need to calculate the energy of the ground state of a helium athom with the variational method using the wave function: $$\psi_{Z_e}(r_1,r_2)=u_{1s,Z_e}(r1)u_{1s, Z_e}(r2)=\frac{1}{\pi}\biggr(\frac{Z_e}{a_0}\biggr)^3e^{-\frac{Z_e(r_1+r_2)}{a_0}}$$ with ##Z_e## the effective charge considered...

Homework Statement determine the center of mass of a thin plate of density 12 and whose shape is the triangle of vertices (1,0), (0,0), (1,1). Then, using the appropriate pappus theorem, calculate the volume of the solid obtained by rotating this region around the line x = -2. Homework...

Hi, in the link https://math.stackexchange.com/questions/1465629/numerically-solving-a-non-linear-pde-by-an-ode-on-the-fourier-coefficients there is a nice example related to spectral theorem using Fourier series. Also in the link...

So I was taught that If gcd (a, p) = 1, then ap-1 ≡ 1 (mod p) And then the proof was Lemma: Let p be prime, Let i, j ,k = Integers If gcd (k, p) = 1 and ik ≡ jk (mod p) then i ≡ j (mod p) Main Proof: Consider 1a, 2a, 3a, ..., (p - 1)a Taking mod p is some arrangement of 1, 2, 3, ..., p - 1 Then...

From an outsiders view, it appears that the old shell theorem is relevant to the dark matter issue: If one views a spherical cluster of galaxies as an interconnected structure, gravity would increase linearly with distance from the center and be greatest at the edge of the cluster. For a spiral...

Hi there. Everyone knows about Torricelli's theorem that says about , in a too big container (opened) the speed of the liquid is given by: v=√(2gh) This result is just for containers that have a hole in the side and the fluid goes out perpendicular to the gravity. And also this result is just...

Homework Statement Homework EquationsThe Attempt at a Solution I don't know how to do part 5, I know the point of maximum speed is at an angle of 120 degrees because the work starts to be negative, but how do I find of the maximum speed at that point without using vector integration? (I...

I was reading the book "Mathematical Methods for Physicists", and in the first chapter, under Gauss's Theorem, the statement given was: The surface integral of a vector over a closed surface equals the volume integral of the divergence of the vector over the entire closed surface. But the in...

Homework Statement Suppose I have a bent coin with a 60% probability of coming up heads. I throw the coin ten times and it comes up heads 8 times. What is the value of the “likelihood” term in Bayes’ Theorem -- the conditional probability of the data given the parameter. Homework...

This may seem rather silly, but how would I go about enunciating Ehrenfest’s theorem? Also, does anyone know what this theorem implies for the relation between classical and quantum mechanics? Any suggestions or help is greatly appreciated!

Homework Statement [/B] Homework Equations Navier strokes theorem The Attempt at a Solution May I ask why would there suddenly a "h" in the highlighted part? "h" wasnt existed in the previous steps, which C2=0 shouldn't add height of the liquid as a constant in the formula... thanks

if I get proof of fundamental laws like Newton's laws of motion or fundamental laws of thermodynamics then will they be laws anymore or will they become theorem. Please tell

I would like to know how to solve the following question: A student answers a question in American test that has m options that are given as follows: In probability P the student has learned the question and therefore knows how to choose the correct answer, otherwise he guesses the question...

Homework Statement ##T(\phi_1\Phi_2\phi_3\Phi_4)## where ## \phi_1## is ##\phi(x_1)## and ##\phi## and ##\Phi## are two different fields. By Wicks theorem ##T(\phi_1\Phi_2\phi_3\Phi_4)= : : + contracted terms.## QUESTION Are the fully contracted terms (apologies for the bad notation I'm...

The diagram below, together with its reversed fermion flow diagram counterpart, collectively sum to zero due to Furry's theorem. I just wanted to understand why this is the case. 1)There are two gluons and one photon attached to the internal line so this is 3 coupled vector current insertions...

Determine an expression for f(x) =(1+x)(1+2x)(1+3x)…(1 +nx),find f⸍(0) .

Non-philosophically inclined experts in relativistic QFT often insist that QFT is a local theory. They are not impressed much by arguments that quantum theory is non-local because such arguments typically rest on philosophical notions such as ontology, reality, hidden variables, or the...

Homework Statement N point particles of mass mα, α = 1,...,N move in their mutual gravitational field. Write down the Lagrangian for this system. Use Noether’s theorem to derive six constants of motion for the system, none of which is the energy Homework Equations Noethers Theorem: If a...

Homework Statement I have never formally studied complex analysis, but I am reading this paper: http://adsabs.harvard.edu/abs/1996MNRAS.283..837S wherein section 2.2 they make use of the residue theorem. I am trying to follow along with this (and have looked up contour integration, cauchy's...

I am reading P.M. Cohn's book: Introduction to Ring Theory (Springer Undergraduate Mathematics Series) ... ... I am currently focused on Section 2.2: Chain Conditions ... which deals with Artinian and Noetherian rings and modules ... ... I need help with understanding an aspect of the proof of...

I am reading P.M. Cohn's book: Introduction to Ring Theory (Springer Undergraduate Mathematics Series) ... ... I am currently focused on Section 2.2: Chain Conditions ... which deals with Artinian and Noetherian rings and modules ... ... I need help with understanding an aspect of the proof of...

I am reading the book: "Advanced Modern Algebra" (Second Edition) by Joseph J. Rotman ... I am currently focused on Chapter 1: Groups I ... I need help with an aspect of the proof of Proposition 1.82 (Correspondence Theorem) ... Proposition 1.82 reads as follows...

I am reading the book: "Advanced Modern Algebra" (Second Edition) by Joseph J. Rotman ... I am currently focused on Chapter 1: Groups I ... I need help with an aspect of the proof of Proposition 1.82 (Correspondence Theorem) ... Proposition 1.82 reads as follows: In the above proof by...

I am reading the book: "Advanced Modern Algebra" (Second Edition) by Joseph J. Rotman ... I am currently focused on Chapter 1: Groups I ... I need help with an aspect of the proof of Proposition 1.82 (Correspondence Theorem) ... Proposition 1.82 reads as follows: In the above proof by...

I am reading the book: "Advanced Modern Algebra" (Second Edition) by Joseph J. Rotman ... I am currently focused on Chapter 1: Groups I ... I need help with an aspect of the proof of Proposition 1.82 (Correspondence Theorem) ... Proposition 1.82 reads as follows: In the above proof by...

Homework Statement find bending stress in x and y dir Homework Equations I = bh^3/12 + ad^2 Stress = Mc/I The Attempt at a Solution I = bh^3/12 + ad^2 Stress = Mc/I see attached calculations My prof gave us a question where we have a motor (20" tall) sitting on a frame with a load of...

I am reading "The Basics of Abstract Algebra" by Paul E. Bland ... ... I am currently focused on Chapter 3: Sets with Two Binary Operations: Rings ... ... I need help with Bland's proof of the Third Isomorphism Theorem for rings ... Bland's Third Isomorphism Theorem for rings and its proof...

I am reading "The Basics of Abstract Algebra" by Paul E. Bland ... ... I am currently focused on Chapter 3: Sets with Two Binary Operations: Rings ... ... I need help with Bland's proof of the Third Isomorphism Theorem for rings ... Bland's Third Isomorphism Theorem for rings and its proof...

I am reading "The Basics of Abstract Algebra" by Paul E. Bland ... ... I am currently focused on Chapter 3: Sets with Two Binary Operations: Rings ... ... I need help with Bland's proof of the Second Isomorphism Theorem for rings ... Bland's Second Isomorphism Theorem for rings and its proof...

I am reading "The Basics of Abstract Algebra" by Paul E. Bland ... ... I am currently focused on Chapter 3: Sets with Two Binary Operations: Rings ... ... I need help with Bland's proof of the Second Isomorphism Theorem for rings ... Bland's Second Isomorphism Theorem for rings and its proof...

Homework Statement I am currently working on a physics experiment to confirm the parallel axis theorem. To do this, I have the following setup: In this experiment I change the distance between the centre of the rotating disc and the central axis. I record the time for 5 complete rotations...

The counter-example is as follows: We have a rectangular toroid ferrite(ring ferrite), magnetized in a closed loop around the ring. We put capacitor plates on top and bottom surfaces, with suitable direction. Now the Poynting vector points inwards or outwards. We look at a cylindrical surface...

I am reading D. J. H. Garling's book: "A Course in Mathematical Analysis: Volume II: Metric and Topological Spaces, Functions of a Vector Variable" ... ... I am focused on Chapter 11: Metric Spaces and Normed Spaces ... ... I need some help with an aspect of the proof of Theorem 11.4.1 ...

I am reading D. J. H. Garling's book: "A Course in Mathematical Analysis: Volume II: Metric and Topological Spaces, Functions of a Vector Variable" ... ... I am focused on Chapter 11: Metric Spaces and Normed Spaces ... ... I need some help with an aspect of the proof of Theorem 11.4.1 ...

Homework Statement Let ##a, b, m, n## be integers with ##\gcd(m,n) = 1##. Let $$c \equiv (b-a)\cdot m^{-1} (\operatorname{mod} n)$$ Prove that ##x = a + cn## is a solution to ##x \equiv a (\operatorname{mod} m)## and ##x \equiv b (\operatorname{mod} n)##, (2.24). and that every solution to...

Hi everybody, Do you think the following reconstruction of Gödel's first incompleteness theorem is basically correct, or at least in the right ballpark? In my view, this incompleteness result basically turns on the mismatch between the indenumerability of the powerset of ℕ and the enumerability...

Hi, Page 166, theorem expressed as 7.2, does anybody know it's name? Many thanks

Homework Statement [/B] I am stuck on the section of my lecture notes attached, where it says that equation 4.20 follows from 4.18 via an application of the fundamental theorem of calculus Homework Equations FoC: if ## f## is cts on ##[a,b]## then the function ...

I am reading Hugo D. Junghenn's book: "A Course in Real Analysis" ... I am currently focused on Chapter 9: "Differentiation on Rn" I need some help with an aspect of Theorem 9.2.1 ... Theorem 9.2.1 reads as follows: Theorem 9.2.1 refers to and relies on Theorem 9.1.10 ... ... so I am...

Homework Statement Homework Equations Stokes Theorem The Attempt at a Solution I'm having a tough time "cancelling" out integrals from both sides of an equation (if possible). On the right hand of the equation, we know since it is a closed curve, that Stoke's Theorem applies and we can...

Let $m$ and $m'$ be positive integers, and $d=gcm(m,m')$. (i) The system: $x \equiv b (mod \ m)$ $x \equiv b' (mod \ m')$ has a solution if and only if $b \equiv b' (mod \ d)$ (ii) two solutions of the system are congruent $mod \ l$, where $l = lcm(m,m')$. I can prove part (i), but can...

Hello all, I have this question I struggle with... EDFB is a parallelogram. It is known that AB/BC = AD/DC. 1) Prove that the parallelogram is a rhombus. 2) It is given that: AB=9, AC=10, BC=AD. Calculate the side of the rhombus. I think I solved the first part. There is a theorem called...

As two particles become closer to each other, the gravitational force (or electric force) approaches infinity. If this is the case, then how does the Shell theorem work? If two particles are extremely close together, there should be an extremely large force. If we then build a sphere around...

Wikipedia says Fermat's last theorem has the greatest number of failed proofs in history. I presume this simple "proof" is one of them. It must have been thought up before me. I first considered it years ago when I first heard of the problem. Figured it was so simple someone else must have...

I have gotten the following answer to (a) and (b) which require verification on them. I have also attached the theorem for reference. (a) Z x Z => have zero divisors The matrix has no zero divisors (no nonzero matrix when multiplied to the matrix gives zero element) Hence not...

Hello, I would like to hear some comments on this: Recently a paper has been published(Sánchez-Kuntz, N. & Nahmad-Achar, E. Found Phys (2018) 48: 27. https://doi.org/10.1007/s10701-017-0126-z) claiming tha QM has a local realist interpretaion. In this paper it is asserted that: "The wave nature...

Dear Every one, In my book, Basic Analysis by Jiri Lebel, the exercise states "show that the sequence $\left\{(n+1)/n\right\}$ is monotone, bounded, and use the monotone convergence theorem to find the limit" My Work: The Proof: Bound The sequence is bounded by 0. $\left|{(n+1)/n}\right|...