Property Definition and 608 Threads

The Schrodinger equation is of the form \frac{d^2 \psi}{dx^2}+[\varepsilon-v(x)] \psi=0. In a lecture, the lecturer said that if we have in a point x_0 , \psi(x_0)=\psi'(x_0)=0 , then \psi(x)=0 .(for a smooth v(x)!) Can anyone give a proof of this? Is it only for a equation of the form...

Hey! (Smile) Is it known that if $p,q$ primes with $p \neq q$ : $$a^p \equiv a \pmod q \Rightarrow a^{p \cdot q} \equiv a^q \pmod q$$ ? If so,why is it like that? Which property is used?

I have heard of various metals and other materials turning from solid to liquid or plasma when temperature and pressure goes up. Is there a metal or other material that goes otherwise , like turns from liquid to solid when temperature and pressure is increased? Is there a material that can...

Homework Statement I am asked to prove that if λ is an eigenvalue of A then λ + k is an eigenvalue of A + kI. The Attempt at a Solution ## A\vec{v}=\lambda\vec{v} ## ## (A+kI)\vec{v}=\lambda\vec{v} ## ## A\vec{v}+k\vec{v} = \lambda\vec{v} ## → ## A\vec{v} = \lambda\vec{v} -...

Difference between physical property and physical quantity?? Hi I'm confused after reading the definitions of physical Quantity and physical property: Definition from wikipedia: physical quantity= is a physical property of a phenomenon, body or substance that can be quantified by...

Ok, we have all read that space is expanding, especially in low mass areas between galaxies, as described by GR. And that mass bends space, like seen in gravitational lensing. My question is whether on larger scales and masses, like on the size of galaxies, space itself is warped? The properties...

Does the log property a*log(x)=log(x^a) still hold if a is even and x I imagine that ln(-1)+ln(-1) can't equal zero, even by some mysterious magic involving complex numbers.

Hey! :o Could you give me a hint how to prove the following property of the Fourier transform, when $F[f(x)]=\widetilde{f}(x)$, where $F[f(x)]$ is the Fourier transform of $f(x)$? $$F[ \widetilde{f}(x) ]= \frac{f(-k)}{2 \pi}$$ We know that: $ \widetilde{f}(k)=\int_{- \infty}^{+ \infty}{...

If I have a relation which is not only antisymmetric (##aRb\rightarrow{}\neg{}bRa##) but it also has a property that ##aRb\land{}bRc\rightarrow{}\neg{}cRa##. How can I be sure that this property holds for any string like that? So that ##aRb\land{}bRc\land{}cRd\rightarrow{}\neg{}dRa## without...

Hello, Does anyone have a reference to a proof of the reflective property of a hyperbola? I need a proof that uses the geometric definition of a hyperbola as the locus of points $X$ such that $|XF_1-XF_2|=2a$ for some fixed points $F_1$ and $F_2$ and a positive constant $a$. The proof may also...

Homework Statement Prove that for every two real numbers x and y ##|x+y| \leq |x| + |y| ##Homework Equations The Attempt at a Solution There are three cases. The easiest ones is when they are both positive and negative. The third one I have problems with. The numbers have different sign. Say...

It is known that:\mathcal{F}\{f\ast g\}=\mathcal{F}\{f\}\mathcal{F}\{g\}\mathcal{F}\{f g\}=\mathcal{F}\{f\}\mathcal\ast{F}\{g\} But this property is valid for inverse tranform too?\mathcal{F}^{-1}\{F\ast G\}=\mathcal{F}^{-1}\{F\} \mathcal{F}^{-1}\{G\}\mathcal{F}^{-1}\{F...

Suppose we have a methereological model which describes the weather change as a Markov chain: we assume that the weather on each day depends only on the weather of the previous day. Suppose further that we extended this model so as to consider season change. defining a different transition table...

Hello, The product of a 2x5 matrix P and a 5x3 matrix B shall be a 2x3 zero matrix. P and B are all matrices of integers. P = [6 2 -5 -6 1;3 6 1 -6 -5] One possible B is [0 -4 0;3 0 0;-1 -1 3;2 -3 -2;1 1 3] This solution B has a property: det(PPt) = det(BtB) = 7778 The question is: What...

Photons demonstrate superposition without having to be isolated from the enviorment. My question is does this only apply to light because I know you can't observe superposition in electrons unless theyre in a vaccum. This is my question in a nutshell. Are there any other propertys that...

Or is it a statistical calculation of where the particle could possibly be. If its a property of nature then it must have a limit, distance at which it seaces to exist. Also a second question does space time exist in QM and if it doesent then why does it exist in the classical world which it...

Use algebraic manipulation to prove that x+yz=(x+y)(x+z) Note that this is the distributive rule, So I have: (x + y)(x + z) = xx + xz + xy + zy = x + xz + xy + zy = x(1 + z + y) zy =x * 1 + (z + y)(zy) = x + ((zzy +...

Is it possible to prove the fact that any function of diagonal matrix is just a function of its element? I don't know how I could express the proof. I can prove that a multiplication of diagonal matrix will just be the multiplication of its element using summation notation, or diagonal matrix...

Hello friends, Most people that I heard put uncertainty as an intrinsic property of the universe which is evident when we make a measurement. But to me it seems that intrinsic property and making a measurement are two entirely different things. If uncertainty were to be just(purely)...

Say for example I discovered how to unify General Relativity with Quantum Mechanics and then someone else uses this improved understanding of physics to engineer a new product which would have been impossible without it. Am I entitled to a portion of the revenue generated by the new product...

Hi All, I'm really curious to know how we can predict the shapes of constant property lines (isenthalpic/constant internal energy/isotherms/isentropes/isobars) on any given plot, such as T-s and P-v or even u-s diagrams. Is there a rule to do so? Usually in practice we deal with p-v and T-s...

Homework Statement How to prove in the easiest way that Klein 4-group is associative. Homework Equations Four elements ##a^2=b^2=c^2=e^2=e##. The Attempt at a Solution If that is group with four elements, how many types of ##a*(b*c)=(a*b)*c## I need to have? 1) ##e*(e*e)=e*e=e##...

Homework Statement We have a finite group ##G## and a homomorphism ##\rho: G \rightarrow \mathbb{GL}_n(\mathbb{R})## where ##n## is a positve integer. I need to show that there's an ##n\times n## positive definite symmetric matrix that satisfies ##\rho(g)^tA\rho(g)=A## for all ##g \in G##...

Homework Statement x''(t)+r*x't+kx=0 Suppose that for some initial conditions the solution is given by x=e^(-2t)*(3cos(t)+4sin(t)) What are are and k? Homework Equations See aboveThe Attempt at a Solution I've tried to "brute force" the solution simply by sticking the expression for x...

How do you show that a linear transformation is idempotent? T:R^3 to R^3 T (x y z)^T = (0.5 (x-z) , y, 0.5 (z-x)) I have no idea where to begin. I know a few facts about idempotent properties e.g such as their eigenvalues are...

[FONT=arial]Prove that a set $A\subset\mathbb{R}^n$ is (Lebesgue) measurable $\iff$ there exist a set $B$ which is an $F_{\sigma}$ and a set $C$ which is a $G_{\delta}$ such that $B\subset A\subset C$ and $C$~$B$ (C without B) is a null set. $F_{\sigma}$ is a countable union of closed sets, and...

Homework Statement The statement that is purported to be true is \frac{a/b}{c/d} = \frac{ad}{bc}Homework Equations The Attempt at a Solution So, I am going along with my proof, and I believe it to be going nicely. However, there is one step that I am unsure of: \frac{\frac{a}{b} d}{c} =...

I'm not sure how they got the RHS of equation 349: where did the |y'(xj)| in the denominator come from? According to (343) the RHS is only f(x0) which in this case is the jth term of the sum that gives y(xj) = 0..

This problem has been taunting me for days now, and I still have no idea of where to start with it... Let \(m\) and \(n\) be non-zero integers. We say that \(k\) is a common divisor of \(m\) and \(n\) if \(k|m\) and \(k|n\). The greatest common divisor of \(m\) and \(n\), denoted as...

Hi everyone, :) I encountered this question and thought about it several hours. I am writing down my answer. I would greatly appreciate if somebody could find a fault in my answer or else confirm it is correct. :) Problem: Let \(V_1,\,\cdots,\,V_k\) be subspaces in a vector space \(V\)...

Are there anybody doing some research on quasicrystals ,especially its mechanical property? I am just wondering why so few people are working on it,because intuitively I think quasicrystals will have a bright future. So what do you think of quasicrystals? Is it worthy of research? I want...

Homework Statement Hello, I know the direct substitution property in calculus. But, the definition of a rational function still confuses me. For example, are these rational functions: y=(x^2+2x+1)/(x+1) y=((x^2+2)^(1/2))/(x+1) The denominator of the first one could cancel. So...

Homework Statement Prove this theorem regarding a property of the Dirac Delta Function: $$\int_{-\infty}^{\infty}f(x)\delta'(x-a)dx=-f'(a)$$ (by using integration by parts) Homework Equations We know that δ(x) can be defined as...

I ran into some formula: ^{a}_{0}∫J_{o}(kr) rdr= a/k J_{1}(ka) How can this be true? What property was used?

Homework Statement Consider the tangent surface of some regular differentiable curve given as X(t,v) = \alpha(t) + v \alpha'(t) . Show that the tangent planes along X(t,constant) are equal. Homework Equations N = \frac{X_{t} \wedge X_{v}}{|X_{t} \wedge X_{v}|} The general tangent...

Hi everyone, :) Trying hard to do a problem recently, I encountered the following question. Hope you can shed some light on it. :) Suppose we have a continuous mapping between two metric spaces; \(f:\, X\rightarrow Y\). Let \(A\) be a subspace of \(X\). Is it true that, \[f(A')=[f(A)]'\]...

So I have been asked to prove a result that is supposedly valid for any norm on any vector space. The statement to prove is: | ||x|| - ||y|| | <= ||x - y|| The problem is, I have no idea where to start with this proof. Maybe I'm missing some fundamental property of norms, but it seems that...

Homework Statement Air has a temperature of 227 Celsius and a pressure of 1000 kPa. Determine the internal energy, quality, enthalpy, and specific volume if it exists. Homework Equations A state is defined by two properties. All other properties can be derived from two independent...

Has anyone seen this before? Is this true? $$ \begin{vmatrix} a & b+c & 1\\ b & a+c & 1\\ c & a+b & 1 \end{vmatrix} = \begin{vmatrix} a & b & 1\\ b & a & 1\\ c & a & 1 \end{vmatrix} + \begin{vmatrix} a & c & 1\\ b & c & 1\\ c & b & 1 \end{vmatrix} $$ In this example this works but I don't know...

Hello, I am embarking to read Spivak's book on Calculus, and have come across some difficulty with something that is perhaps rather trivial. In the third edition, there is a section entitled Basic Properties of Numbers. Near the end of page 7, the author begins discussing how he will use...

Prove the following logic property using a Truth Table (perfect induction). What is this property called? x + y * z = (x + y)(x + z) My Answer: Distributive Property? Truth table. x y z f [0]0 0 0 0 [1]0 0 1 0 [2]0 1 0 0 [3]0 1 1 1 [4]1 0 0 0 [5]1 0 1 1 [6]1 1 0 0 [7]1 1 1 1 By truth...

Hi, I'm following the proof of the "Scaling Property of the Fourier Transform" from here: http://www.thefouriertransform.com/transform/properties.php ...but don't understand how they went from the integral to the right hand term here: The definition of the Fourier Trasform they...

Attached is a copy of p181 of Strauss Partial Differential Equation. This is part of proof of Mean Value Property using Green's 1st identity: \int_Dv\nabla u+\nabla v\cdot\nabla u \;dV=\oint_A v\frac {\partial u}{\partial r}dA Let ##v=1## and let ##u(r,\theta,\phi)## be a harmonic function ie...

Ok, I don't think I'm on the right track here. I ASSUMED that the set of all countable collections \{I_k\}_{k = 1}^\infty of nonempty open, bounded intervals such that E \subseteq \bigcup_{k = 1}^\infty I_k is a countable set itself, which it probably isn't. I'm not even sure where to start...

Can you explain what this image is saying. I'm confused.

So there is a proof that the sum of any two even numbers is an even number. 2k + 2l = 2(k +l) We have written the sum as 2 times an integer. Therefore the sum of any two even numbers is an even number. An essential part of this proof is that k + l is an integer. How do we know this? Is it an...

Hi I am not sure where to post this question but I am trying to simplify this expression: r*c'w+c (As in R AND NOT C AND W OR C) to c+wr (As in C OR W AND R) and I know that it simplifies to this and they are both equivalent; however my question is which boolean simplification property is...

hello! I'm trying to understand the following property: Let X and Y be independent random variables z: = X + Y. Then http://imageshack.us/a/img268/9228/71pe.png where fZ (z) is the probability mass function for a discrete random variable defined as follows...

Recently I review some old text and browse around the internet to read about definition of strain and stress. I come across the following document http://web.mit.edu/emech/dontindex-build/full-text/emechbk_4.pdf Previously I have been facing difficulty trying to come out with an...

Suppose you have the following definition of Dirac-delta function, or the so called sifting property: \int^{d}_{c}f(t)δ(t-a)dt =\left\{\begin{array}{cc}f(a),&\mbox{ if } c\leq x \leq d\\0, & \mbox{ if } x>d \mbox{ or } x<c \\ \mbox{undefined}, & \mbox {if } x = d \mbox{ or } x = c...