Condition Definition and 587 Threads

given the generalized SL conditions Let's say psi_m and psi_n are eigenfunctions of the given y. Its Wronskian is 0 because otherwise the boundary condition doesn't make sense much. However, I wonder if it is possible to have, S={ x | W[psi_m(x) , psi_n(x)] =/= 0 } otherwise...

Somebody told me that the condition that must be met for Quantum Entanglement in a system, is that the sum of the wavefunctions of the individual particles must equal the overall wavefunction of the system. But isn't this the case anyways with any system of two particles whether they are...

Im reading Carroll's Spacetime and Geometry section 4.2 where he claims the following as the weak energy condition: Given a energy momentum tensor T and a timelike vector t then Tμν tμ tν ≥ 0. He claims that for a perfect fluid this is equivalent to the statement that ρ ≥ 0 and (ρ+P) ≥ 0...

Homework Statement The Hamiltonian for an atom of deuteron is ##\hat{H} = \frac{-\hbar^2 \nabla_R^2}{2M} - \frac{\hbar^2 \nabla^2}{2\mu} - Ae^{\frac{-r}{a}}## Where ##\nabla_R## is the differential operator for the centre of mass co-ordinates ##R = \frac{m_p\vec{r_p} + m_n\vec{r_n}}{M}## and...

My Quantum Field Theory notes, after explaining the Lorentz condition, say this: I have some questions about this. 1) What exactly does the polarization of a photon mean? 2) Why do the degrees of freedom of the potentials determine the polarizations of the photon? 3) If instead of the Lorentz...

I am not a scientist, but as a hobby I am summarizing different initial condition theories, specifically, eternal inflation, LGC, cyclic, and bounce theories. I need a completion time ATB where all theories produce an identical plasma. The plasma then enters the big bang process of expansion...

I'm learning vector calculus and am wondering how general it is. The appear to be using a smoothness condition, but what is it? Certainly the functions are required to have two derivatives. That is, the partial derivatives can be taken twice. Are they further required to have an infinite...

Homework Statement I have the solution to the heat equation, with the BC's and everything but the IC applied. So I am just trying to solve for the coefficients, the solution without the coefficients is $$u(x,t) = \sum_{n=1}^{\infty} A_n\sin(nx)e^{-n^2t}$$ If the initial condition is ##u(x,0) =...

A person of 60 kg is holding on a rope of 3m while standing on a the ledge of a building of height 7m. The rope is fixed to a point at roughly eye level 3 m from ledge. The person walks off the building and is swung in a vertical circle. If the person let's go at approximately the same height he...

Homework Statement Find the tension T needed to hold the cart shown (pic included) in equilibrium, no friction. Using virtual work, and force components. (I don't care about signs, just looking for the magnitude of tension with quick reasoning) (not homework, just studying virtual work)...

Homework Statement :[/B] I would like to know if the definition of the ZSR response means that the initial condition at any t0 needs to be 0.Homework Equations :[/B] let's say : we're trying to calculate the ZSR response from a first order equation of the voltage of a capacitor and the initial...

Alright, so now that I think have some more "mathematical maturity", I have decided to go back and review/re-learn multivariable calculus. I've just started, and have gotten to differentiation. From what I have seen, most books state the following sufficient condition for differentiability: A...

Hello In Newtonian theory Poisson's equation holds: ## \nabla ^{2} U = 4 \pi G \rho ##. So: given a density ##\rho ##, it is possible to find a potential U. On the other hand, I can choose a random function U and give it a gravitational significance if it gives, by Poisson's eq., a density...

http://local.eleceng.uct.ac.za/courses/EEE3055F/lecture_notes/2011_old/eee3055f_Ch4_2up.pdf (Page 4.4 )I am having a trouble with understanding why closed loop line integration is 0 at dielectric boundary. As far as I know, closed loop line integration is 0 because electric field is...

Homework Statement I think, to normalize a wavefunction, we integrate over the solid angle ##r^2 dr d\theta d\phi##. Typically we have ## R(r)Y(\theta, \phi) ## as solutions. If ##Y## is properly normalized, then the normalization condition for ##R(r)## ought to be $$ \int_0^\infty dr r^2...

Homework Statement Consider the boundary value problem \begin{equation} u''(t)=-4u+3sin(t),u(0)=1,u(2)=2sin(4)+sin(2)+cos(4) \end{equation} Homework Equations Derive the linear system that arise when discretizating this problem using \begin{equation} u''(t)=\frac{u(t-h)-2u(t)+u(t+h)}{h^2}...

I am reading the book "An Introduction to Rings and Modules with K-theory in View" by A.J. Berrick and M.E. Keating ... ... I am currently focused on Chapter 3; Noetherian Rings and Polynomial Rings. I need someone to help me to fully understand the maximal condition for modules and its...

We have never discussed about constant mechanical power transfer for the linear case, as against rotational well documented gear transmission. The energy acquired by linear motion, if varies linearly, then 0.5mv^2 must have constant differential. Trying it, if u=0, v=at...

Homework Statement 1 mm3 of gas at normal pressure and temperature contains about 1015 particles. Considering the particles as point-like and classical, provide a rough, conservative estimate for how many hard drives would be necessary to store the initial conditions of all gas particles. (As...

Homework Statement Let p: x and y satisfy inequality x2 + y2 + 4x - 8y + c < 0 where c is real number q: x and y satisfy x - y + 8 > 0 ; 4x + 3y - 24 < 0 ; y < 0 Find the range of c so that: a. p is sufficient condition for q b. p is necessary condition for q Homework Equations Circle...

Not sure I understand this question, which says: "Develop a condition when 2 forces are parallel, with & without using Cartesian co-ords." I think there must be a common normal between the 2, so that $ F_1.\vec{n} = 0 = F_2. (- \vec{n}) $ or $ (F_1 + F_2).\vec{n} = 0 $ - is that correct...

I am reading the book "An Introduction to Rings and Modules with K-theory in View" by A.J. Berrick and M.E. Keating ... ... I am currently focused on Chapter 3; Noetherian Rings and Polynomial Rings. I need someone to help me to fully understand the maximal condition for modules and its...

Beginning with the Schrodinger equation for N particles in one dimension interacting via a δ-function potential ##(-\sum_{1}^{N}\frac{\partial^2}{\partial x_i^2}+2c\sum_{<i,j>}\delta(x_i-x_j))\psi=E\psi## The boundary condition equivalent to the ##\delta## function potential is...

Please help me solve this differential equation for the initial condition (0,-1): dx/dy = ((1+x^2)^(1/2))/(xy^3) I think I'm doing something wrong because I end up with ((x^2)(y^3))/2 = ((x^2)+y)^(1/2) + c, but when plugging in the initial condition it ends up being the square root of...

Hello! I need to understand one seemingly simple thing in wave mechanics, so any help is much appreciated! When a pulse travels to the right toward an open end(like a massless ring that is free to oscillate only in the vertical direction), then when the wave reaches the end it gets reflected and...

I'm sorry for my bad English. Let X a completely Hausdorff space. Will the be space of all continuous real-valued functions on a space X with the topology of pointwise convergence dense in the Tychonoff product ℝX?

Hello! (Wave) Does the following $f(t,y)$ satisfy the Lipschitz condition as for $y$, uniformly as for $t$? If so, find the Lipschitz constant. $$f(t,y)=\frac{|y|}{t}, t \in [-1,1]$$ I have tried the following: $$\frac{|f(t,y_1)-f(t,y_2)|}{|y_1-y_2|}=\frac{|y_1|-|y_2|}{t|y_1-y_2|} \leq -...

I have a question about an integral taken from integral tables of Gradshteyn and Ryzhik precisely , 3,914 -1 ( pag.490 ): http://www.lepp.cornell.edu/~ib38/tmp/reading/Table_of_Integrals_Series_and_Products_Tablicy_Integralov_Summ_Rjadov_I_Proizvedennij_Engl._2.pdf The condition to use the...

**Observations:** Given a power Diophantine equation of ##k## variables and there exists a “general solution” (provides infinite integer solutions) to the equation which makes the equation true for any integer. 1. The “general solution” (provides infinite integer solutions) is an...

According to the experimental curve of Binding Energy per nucleon vs Mass no. , we have come to know that heavier nuclei having less B.E. are fissionable. We have also learned from Neutron vs Proton curve that those nuclei having N/P>1 can show radioactivity. But my question is why not all heavy...

Hi I'm trying to use Peierl's argument which in essence is clear to prove that there does exist a phase transition in the 2D Ising model without external field. The issue I'm having is of a more mathematical nature, in class it was mentioned that there is a phase transition if for some ##\delta...

Hi, I know, there is a stability condition for solving the Convection-Diffusion equation by Finite Difference explicit/implicit technique, which is \Delta t<=(\Delta x)^2/(2*D) for one-dimensional or \Delta t<=((\Delta x)^2+(\Delta y)^2)/(8*D) for two-dimensional problem, where D is the...

I am interested in locating a material that can withstand a strong alkaline medium (10 M KOH) and approx. 5 atm pressure... I am somewhat new to material chemistry so all I have been able to think of thus far is PVC pipe. Through my research I have discovered that PVC is highly fire retardant...

I'm a novice studying laser physics and I came a across the condition for optical gain: \frac{N_2}{g_2} > \frac{N_1}{g_1} This is a basic set up where N_1 is the number of atoms in the lower energy state and N_2 is the number of atoms in the higher energy state. g_1, and g_2 are the...

Homework Statement A homogeneous wooden bar of length 10 cm, thickness 4 cm and weight 1 Kg is balanced on the top of a semicircular cylinder of radius R as shown below. Calculate the minimum radius of the semicircular cylinder if the wooden bar is at stable...

Suppose we have an RC series dc circuit with two capacitors C1 and C2 and resistance R. If the switch is closed at t=0, all the voltage appears across R initially. Fine.. But how does it reach across R through two insulation barriers (breaks) in the circuit? I can understand the mechanism for...

If the switch in an RL dc circuit is closed at t=0, the current i in the inductor rises exponentially. But at t=0, i=0 because the inductor generates a back emf equal to the applied voltage at t=0. So in absence of any current,how does the inductor come to know that the switch has been closed...

In my textbook one of the conditions for formation of ionic bond is given as The cation should be large and anion should be small But in the image of Nacl lattice structure ,we can see that it is other way around I am not getting the reason,Is my textbook wrong ? Or it has something to do with...

For any 2 pairs of points (xe,ye) & (xs,ys), I can fit various equiangular spiral through those 2 points based on the equation r = ke^(aθ). A typical one is illustrated below: Then, I can vary the origin of the spiral -> i.e. (xc,yc) to generate another equiangular spiral which passes through...

Homework Statement Here is a link to the proof I am reading: https://www.math.ucdavis.edu/~hunter/m125b/ch1.pdf Homework EquationsThe Attempt at a Solution The proof to which I am referring can be found on pages 8-9. At the top of page 9, the author makes an assertion which I endeavored to...

For β- we have: ##M(A,Z)>M(A,Z+1) + m_{e} - m_{e}## An electron is removed from the atom and therefore we need to take that away from the M(A,Z+1) term But for β+ we have been given: ##M(A,Z)>M(A,Z+1) + m_{e} + m_{e}## What is this saying? A positron is emitted, therefore shouldn't we minus...

While reading some articles on Wikipedia I came upon one interesting statement that essential says (I've rephrased for clarity; correct me if I'm wrong): "The Time-asymmetry of the second law of thermodynamics is due to the initial conditions of our universe" Can someone elaborate on what...

Can @Drakkith , @Doc Al and others help me in this? In YDSE, if s is the size of source slit and S is the distance between source slit and the double slits, Then why condition s/S <= λ/d must be satisfied to observe fringes? Here λ is wavelength of light source and d is the distance between two...

Hi all! I was wondering what the necessary condition is for two arbitrary matrices, say A and B, to commute: AB = BA. I know of several sufficient conditions (e.g. that A, B be diagonal, that they are symmetric and their product is symmetric etc), but I can't think of a necessary one. Thanks...

Hi, I am trying to use NDSolve in Mathematica to solve a set of differential-algebraic equations: NDSolve[{-6250 f[t] + 0.025 p[t]^2 f[t] + 0.1 f[t]^3 + 3 q[t] f'[t] + f''[t] == 0, 1.5230870989335428*^-35 p[t]^4 + q'[t] == 0, -4.32*^36 q[t]^2 + 10/3 \[Pi]^2 p[t]^4 + 0.0125 p[t]^2...

Hi, My final goal is to solve numerically Schrodinger's equation in 3D with some potential for the unbounded states, meaning that far away from the potential (at infinity) we may find a free wave and not something that goes to zero. The basic idea is that I have a particle in (0,0,0) that...

y''-10y'+25=0 Solve the ODE with initial condition: y(0) = 0, y' (1) = 12e^5 . I keep getting y=12/5e^5x when c1=0 and c2=12/5 ... but Answer key says y=2xe^5x what am I doing wrong?

I want to calculate the torque coming onto a half shaft in a very particular event. The event is I let's say I am in 3rd gear and have reached my max torque zone after which I have taken my foot of the acc pedal...nw I m letting the the vehicle coast as soon as it reaches say 60% of max power...

By wave-guides I refer to the device with (perfectly) conducting walls that enclose EM wave inside. I'm reading this tutorial here http://farside.ph.utexas.edu/teaching/em/lectures/node105.html and found this interesting boundary condition for wave-guides: ##E_{\parallel} = 0## -- (1)...

Hello! (Smile) I want to find the exact solution of the recurrence relation: $T(n)=2T(\sqrt{n})+1$.$$m=\lg n \Rightarrow 2^m=n \\ \ \ \ \ \ \ \ \ 2^{\frac{m}{2}}=\sqrt{n}$$ So we have: $T(2^m)=2T(2^{\frac{m}{2}})+1$ We set $T(2^m)=S(m)$, so we get: $S(m)=2S \left( \frac{m}{2}\right)+1$...