Function Definition and 1000 Threads

Prove directly that the transformation $$Q_{1} = q_{1}, P_{1} = p_{1} − 2p_{2}$$ $$Q_{2} = p_{2}, P_{2} = −2q_{1} − q_{2}$$ is canonical and find a generating functionSo the first part is easy and can be skipped here. I have some difficults regarding the second part, namely, the one that ask for...

Hi PF! I have a function ##f(s,\theta) = r(s,\theta)\hat r + t(s,\theta)\hat \theta + z(s,\theta)\hat z##. How can I plot such a thing in Mathematica? Surely there's an easier way than decomposing ##\hat r, \hat \theta## into their ##\hat x,\hat y## components and then using ParametricPlot3D?

So what am I doing wrong here? I can clearly observe it, I'm nearly sure I can tell which particles are going throw each slit if I used another laser too. My suspicion is that the electrical current of the photon detector that uses germanium or silicon to detect the particles are influencing the...

Hello! So, I was beginning to skim Kleppner and Kolenkow for an upcoming course I’m taking over the summer. I saw this on pg. 17 and was wondering if I’m making a silly mistake in understanding what the book is saying. When they take the derivative of the position function, isn’t the velocity...

So the Langevin equation of Brownian motion is a stochastic differential equation defined as $$m {d \textbf{v} \over{dt} } = - \lambda \textbf{v} + \eta(t)$$ where the noise function eta has correlation function $$\langle \eta_i(t) \eta_j(t') \rangle=2 \lambda k_B T \delta_{ij} \delta(t -...

Homework Statement:: Find the interference function ##I(\delta)## where The emission is analyze by a Michelson interferometer. Relevant Equations:: ##I(\delta) = \frac{1}{2} \int_{-\infty}^{\infty} G(k) r^{ik \delta} dk## ##I(\vec{r}) = I_1 + I_i + 2 \sqrt(I_1 I_i) cos (k\delta)## I have 5...

I came across this question on chegg for practice as I'm self learning complex analysis, but became stumped on it and without access to the solution am unable to check. Let $$ f(z)=\frac{cos(z)} {(z-π/2)^7} $$. Then the singularity is at π/2. And on first appearance, it looks like a pole of...

Hello, I try to solve a time dependent problem described by a Hamiltonian of the type $$ \mathcal{H}(t) = H_0 + V \delta(t) .$$ I started by trying to solve the Schrödinger equation with ##H_0 = p^2 / 2m##, but I'm getting a bit stuck. I would like to know if you know of any books that deal...

Hi, I was working through the following problem and I am getting confused with the solution's definition of the dual. Problem: Given the optimization problem: minimize ## x^2 + 1 ## s.t. ## (x - 2) (x - 4) \leq 0 ## Attempt: I can define the Lagrangian as: L(x, \lambda) = (x^2 + 1) + \lambda...

I just want to be certain, i think the inequality indicated is not correct...ought to be less than. Kindly confirm...This is a textbook literature.

Hi, PF, want to know how can I go from a certain error formula for linearization I understand, to another I do not Error formula for linearization I understand: If ##f''(t)## exists for all ##t## in an interval containing ##a## and ##x##, then there exists some point ##s## between ##a## and...

Hi, I have some question about evaluating a cosine function from ##-\infty## to ##\infty##. I saw for a cosine function evaluate from ##-\infty## to ##\infty## I can change the limits from 0 to ##\infty##. I have a idea why, but I can't convince myself, furthermore, is it always the case no...

Suppose i measure the phase and amplitude of some radiation, this might be a coherent state of an entangled state, how would i construct the Wigner function from these measurements?

At first, I inputted h(t), of which I solved for, into the mass flow rate formula. So it looked something like this, m-dot(t) = -(density)*[sqrt(g*(H-(g*d^4*t^2/D^4)]*(pi/4)*d^2 But I don't think that's right? Any thoughts?

Will it be [{(r-a)/r}*H(r-a)]

Hi, I found Laplace transform of this Dirac delta function which is ##F(s) = e^{-st}## since ##\int_{\infty}^{-\infty} f(t) \delta (t-a) dt = f(a)## and that ##\delta(x) = 0## if ##x \neq 0## Then the Mellin transform ##f(t) = \frac{1}{2 \pi i} \int_{\gamma - i \omega}^{\gamma +i \omega}...

I would like a program to read in a file entered by the user via the command line, which is then used in the main body of the code. See example code below: #include <iostream> #include <fstream> struct run_t { std::string file; }; run_t run; const POINTER* ptr = toy(run.file,0); int...

Is there a general expression for the wave function $\psi$, which describes the electronic properties of an arbitrary covalent bond? For example is it equal to some sort of trigonometric expression?

Hi PF! I followed someone's help on here and have the following code in python that performs monte carlo integration from math import * from random import * def integrate(alpha): # MONTE CARLO INTEGRATION OVER NON-RECTANGULAR DOMAINS def f(pt): # RETURN INTEGRAND AS FUNCTION...

So I've just started learning about Greens functions and I think there is some confusion. We start with the Stokes equations in Cartesian coords for a point force. $$-\nabla \textbf{P} + \nu \nabla^2 \textbf{u} + \textbf{F}\delta(\textbf{x})=0$$ $$\nabla \cdot \textbf{u}=0$$ We can apply the...

Hi, I am having to refresh my oscilloscope knowledge and am confused about one last function generator setting... Burst period. If I have 1 cycle at say 700 kHz it is 1.43us. If I set number of cycles to 10 then that is 10 * 1.43us = 14.3us time. This is my ON burst. So what is the burst...

Hi PF! Given the following ODE $$(p(x)y')' + q(x)y = 0$$ where ##p(x) = 1-x^2## and ##q(x) = 2-1/(1-x^2)## subject to $$y'(a) + \sec(a)\tan(a)y(a) = 0$$ and $$|y(b)| < \infty,$$ where ##a = \sqrt{1-\cos^2\alpha} : \alpha \in (0,\pi)## and ##b = 1##, what is the Green's function? This is the...

Hi PF! I'm numerically integrating over a Green's function along with a few very odd functions. What I have looks like this NIntegrate[-(1/((-1.` + x)^2 (1.` + x)^2 (1.` + y)^2)) 3.9787262092516675`*^14 (3.9999999999999907` + x (-14.99999999999903` + x (20.00000000000097` -...

I have a question about statistical physics. Suppose we have a closed container with two compartments, each with volume V , in thermal contact with a heat bath at temperature T, and we discuss the problem from the perspective of a canonic ensemble. At a certain moment the separating wall is...

hi guys I am recently taking a Nuclear structure course, and have a lot of questions regarding the nuclear rotor model. in most nuclear physics books the I have, the wave function associated with the rotor model of the nucleus is written in terms of the Wigner D functions , like the expression...

I want to determine the normal flow depth in a perfectly horizontal circular conduit. The system characteristics are known (Internal pipe diameter, Mannings roughness, Discharge). However, I am not sure how to calculate the normal flow depth. When using Manning's equation one can find the normal...

From my reading of several quantum optics textbooks and spectroscopy texbooks, the emission and absorption spectrum of an atom or molecule are always given in terms of the time-correlation function, for example the emission spectrum of a two level atom is given by: $$...

this is how i try to solve it: can someone please help me with that because i don't know what I am doing worng here.

Write and test the fib function in two linked files (Fib.asm, fib_main.asm). Your solution must be made up of a function called fib(N, &array) to store the first N elements of the Fibonacci sequence into an array in memory. The value N is passed in $a0, and the address of the array is passed in...

Given a wavefunction ψ(x, 0) of a free particle at initial time t=0, I need to write the general expression of the function at time t. I used a Fourier transform of ψ(x, t) in terms of ψ(p, t), but, i don't understand how to use green's functions and the time dependent schrodinger equation to...

Hi, I was reading through some slides about graph clustering. In the slides was a very short discussion about 'eigenvectors and segmentation'. I don't quite understand where one of the formulae comes from. Context: We have some undirected graph with an affinity matrix (i.e. weighted adjacency...

Hello all, see below for a snippet of a header file, class1.h, and source code file, class1.cpp, adjusted to reproduce the issue I am having. I have declared a series of functions in the .h file and their corresponding definitions in the .cpp file but when I compile I get the error...

Hi, I was looking at the following example, and I cannot really understand the justification for why this function is positive semi-definite. Example Problem: We are looking at the function: ## f(x, y) = \frac{x^2}{y}, x \in \mathbb{R} , y > 0 ##. Is this function positive semi-definite...

help me please to determine what are the equations i need tofinish my activity. Thankyou

I tried to code spinoperators who act like $S_x^iS_x^j$ (y and z too) and to apply them to the states, which works fine. I am not sure about how to code the expectation value in the product Space. Has anyone pseudo Code to demonstrate that?

Could anyone please help me I am especially stuck on the second part of the question. Thanks very much I really appreciate it.

Im having trouble understanding the wording to this problem. When it says "from r=0 to r=infinity". My Qenc would zero out. I guess it makes sense that from infinitely far away you wouldn't "feel' the electric field but considering this question leads to 4 other questions I don't think I am...

What I do is set the two equations equal to one another and solve for z. This gives: $$z = \sqrt{x^2+2y^2-4x}$$ which is a surface and not a curve. What am I doing wrong?

It is asking to derive the time-independent wave function and has managed to get the answer of and i am very confused as where (ix/a) and (-x^2/2a) came from ? Thanks.

Greetings! My question is: is it possible to use the green theorem to compute the circulation while in presence of a scalar function ? I know how to solve by parametrising each part but just in case we can go faster? thank you!

I have to find 2 solutions of this Bessel's function using a power series. ##x^2 d^2y/dx^2 + x dy/dx+ (x^2 -9/4)y = 0## I'm using Frobenius method. What I did so far I put the function in the standard form and we have a singularity at x=0. Then using ##y(x) = (x-x_0)^p \sum(a_n)(x-x_0)^n##...

Greetings! Here is the solution that I understand very well I reach a point I think the Professor has mad a mistake , which I need to confirm after putting x-1=t we found: But in this line I think there is error of factorization because we still need and (-1)^(n+1) over 3^n Thank you...

Before starting, I will leave the link to the article I am talking about here: http://www.msc.univ-paris-diderot.fr/~phyexp/uploads/LaimantParesseux/aimant2.pdf I am conducting a similar experiment to the one discussed in the paper above. Basically, I am rolling a neodium supermagnet down a...

In an article written by Richard Rollleigh, published in 2010 entitled The Double Slit Experiment and Quantum Mechanics, he argues as follows: "For something to be predictable, it must be a consistent measurement result. The positions at which individual particles land on the screen are not...

I am desperate. I've scoured the web for the formula for the probability density function for the interference pattern obtained in the double slit experiment with both slits open. So I want to know the probability density function and not the intensity function. I prefer not to have references...

Hey! :giggle: For $n \in \mathbb{N}$ we consider the discrete statistical product model $(X ,(P_{\theta})_{\theta \in\Theta})$ with $X = \mathbb{N}^n$, $\Theta = (0, 1)$ and $p_{\theta}(x_i) = \theta(1 -\theta)^{x_i−1}$ for all $x_i \in \mathbb{N}, \theta \in \Theta$. So $n$ independent...

Hello I have a script a13_roman2num.py that reads def value(r): if (r == 'I'): return 1 if (r == 'V'): return 5 if (r == 'X'): return 10 if (r == 'L'): return 50 if (r == 'C'): return 100 if (r == 'D'): return 500 if...

I tried using substitution ##u=\sqrt{16x-x^8}##, didn't work Tried factorize ##x## from the denominator and then used ##u=\sqrt{16-x^7}##, didn't work Tried using ##u=x^4## also didn't work How to approach this question? Thanks

I think the answer is an even function as the function ##x^2## is an even function and thus, is symmetrical w.r.t. Y axis. The question I have is how to do this problem algebraically. I tried to graph some functions on GeoGebra to verify my answer. a) ##y = ln(x^2)## b) ##y = sin(x^2)##...