1d Definition and 417 Threads

A) I just did what it said to do: $$\sin\left(4x_{1}\right)=1\implies x_{1}=\frac{\arcsin\left(1\right)}{4}\ m=\frac{\pi}{8}\ m\approx 0.392699081699\ m$$ B) I modified the method from an example from the lecture the other week: $$U\left(x\right)=-\int...

[mentor's note - moved from one of the homework help forums] Homework Statement:: It's a question. Relevant Equations:: Vector calculus. Is it true to say that in one dimension I can show vector quantities using ±number instead of a vector? ± can show possible directions in one dimension and...

Hey, I am looking for a derivation of time-dilatation or some trivially equivalent formulas (Lorentz-transformation, conservation of 4-distance (edit: invariance of spacetime interval) etc) in 1 dimension, using that c is observer independent. I only can find the one that uses a light-clock...

Hello everyone, I'm trying to solve the transient heat transfer problem within the ID wall. The material is steel, and it is isotropic. The properties are given below : L = 5 mm qin = 0 Tinf = 100 deg C Tini = 20 deg C rho = 7850 kg/m3 cp = 460 W/Kg.K k = 45.8 W/m.K h = 20 W/m^2.K alpha = k /...

Suppose $$ D=\{ (x,0) \in \mathbb{R}^2 : x \in \mathbb{R}\} \cup \{ (0,y) \in \mathbb{R}^2 : y \in \mathbb{R} \}$$ is a subset of $$\mathbb{R}^2 $$ with subspace topology. Can this be a 1d or 2d manifold? Thank you!

I know I need to look at the conversation of momentum, as well as the conservation of kinetic energy. However I get stuck with my equations. Any help would be greatly appreciated! I've already got (don't know where I am going wrong): (v)^2 + (1/2)(m)(v)^2 = (vf1)^2 + (1/2)(m)(vf2)^2 (3/2)v^2 =...

For the 1 dimensional wave equation, $$\frac{\partial^2 u}{\partial x ^2} - \frac{1}{c^2}\frac{\partial ^2 u }{\partial t^2} = 0$$ ##u## is of the form ##u(x \pm ct)## For the 3 dimensional wave equation however, $$\nabla ^2 u - \frac{1}{c^2}\frac{\partial ^2 u }{\partial t^2} = 0$$It appears...

Hi, Forgive me for the crowded drawing, but please reference the attached screenshot. Let’s say I have 2 plates bolted together by some bolts (red), and on the inside is a pressure w pushing the top plate up, in psi (lb/in^2). In order to get an estimate for the maximum distance between bolts...

Greetings everyone, Exactly as the title says. I am reaching to something strange and I do not know what I am missing. It must be something obvious... case 1: -L/2 to L/2 After taking the Schrodinger equation and considering potential equal to zero inside we reach at this...

Reif,pg 14. ##n_1## is the number of steps to the right in a 1D random walk. ##N## are the total number of steps "When ##N## is large, the binomial probability distribution ##W\left(n_{1}\right)## ##W\left(n_{1}\right)=\frac{N !}{n_{1} !\left(N-n_{1}\right) !} p^{n_{1}} q^{N-n_{1}}## tends to...

##v=\frac12 *1*4+\frac12*1*4= 4 m/s## but the answer is wrong.

1 = elephant 2 = fly So I am trying to find v'2 which is the final velocity of the fly. I have v1 the initial velocity of the elephant 2.1m/s. So I plug it into the equation and have v'2=(2m1/(m1+m2))*2.1m/s. We are not given the masses so I just know m1>m2 but I don't understand how that will...

##x## can be discretized as ##x \rightarrow x_k ## such that ##x_{k + 1} = x_k + dx## with a positive integer ##k##. Throughout we may assume that ##dx## is finite, albeit tiny. By applying the Taylor expansion of the wavefunction ##\psi_n(x_{k+1})## and ##\psi_n(x_{k-1})##, we can quickly...

I want to develop a 2D random field and its change with time with constant velocity. My process: 1. Define a 2D grid [x, y] with n \times n points 2. Define 1D time axis [t] with n_t elements 3. Find the lagrangian distance between the points in space with the velocity in x and y ...

Good day. We know how simple objects, such as 1D wires behave when a simple harmonic wave travels along a wire, or two wires knotted togethe.We also know what happens if you excite a circular thin disc with a single frequency. Are there some material I can read on, that considers the effect...

Attempt at a solution: \begin{aligned}Z=\sum ^{N}_{r=0}C\left( N,r\right) e^{-\beta \left[ -NJ+2rJ\right] }\\ \Rightarrow Z=e^{\beta NJ}\sum ^{N}_{r=0}C\left( N,r\right) e^{-2\beta rJ}\end{aligned} Let ##e^{-2\beta J}=x##. Then ##e^{-2\beta rJ}=x^{r}##. \begin{aligned}\therefore Z=e^{\beta...

Can we apply the 1d equation (dE/dx = labmda/epsilon0)dEdx=λϵ0 to the first and the second figures? But, in the 2nd case, if we integrate the charge density, some field exists between the two charge densities. Intuitively, it should be like the last figure. What's wrong with this?

I am struggling to understand shocks in a one dimensional lattice with a linear spring connecting the masses. Say I have a one dimensional lattice with a linear spring constant, k and lattice spacing a. If the particles in the lattice has mass, m then my speed of sound c is a*sqrt(k/m). That is...

The 1D transverse field Ising model $$ H(\sigma)=-J\sum_{i\in \mathbb{Z}} \sigma^x_i \sigma^x_{i+1} -h \sum_{i \in \mathbb{Z}} \sigma^z_i$$ is usually solved in quantum way, but we can also solve it classically - e.g. parametrize angles of spins ##\sigma^x_i = \cos(\alpha_i)...

(3) To solve the initial value problem $$\begin{cases} \partial_t\phi-\partial^2_x\phi=0 & \text{in}\quad (0,\infty)\times R \\ \phi(0,\cdot)=\psi & \text{on}\quad \{t=0\}\times R \end{cases}$$ we use the fundamental solution in 1D $$\Phi_1(t,x)=\frac{1}{\sqrt{4\pi...

a proton is confined to an infinite potential well of width ##a=8fm##. The proton is in the state $$\psi(x,0)=\sqrt{\frac{4}{56}}sin\Big(\frac{\pi x}{8}\Big)+\sqrt{\frac{2}{56}}sin\Big(\frac{2\pi x}{8}\Big)+\sqrt{\frac{8}{56}}sin\Big(\frac{3\pi x}{8}\Big)$$ (a) What are the values of energy...

Hello everybody at the forum I'm from Ukraine, I have Chemistry degree, and last year I began to self studying Quantum Mechanics. I'm reading this article: R. Garcia, A. Zozulya, and J. Stickney, “MATLAB codes for teaching quantum physics: Part 1,” [Online]. Available...

I have no idea about a possible solution, please help me :)

This is my c program below. Again everything works as expected up until the highlighted lines or the second for loop. When i run my program to output the arrays contents i get bizarre numbers that are not correct. # include <math.h> # include <stdlib.h> # include <stdio.h> # include <time.h>int...

In 1D Photonic crystals, a defect can be introduced to create a defect/resonance mode and enable transmission. At first considerations, the thickness of the single defect layer determines the transmission frequency. Moreover, if it is a half-wavelength layer it will enable a resonance condition...

So I've managed to confuse myself on this problem :) Since the problem says we can assume ##m_p << m_b##, I'm assuming that the velocity of the bowling ball will be unchanged, such that ##\vec v_{b,i} = \vec v_{b,f} = -v_{b,0} \hat i## I started out using the energy-momentum principle, ##(\vec...

I am currently trying to compute the Green's function matrix of an infinite lattice with a periodicity in 1 dimension in the tight binding model. I have matrix ##V## that describes the hopping of electrons within each unit cell, and a matrix ##W## that describes the hopping between unit cells...

Okay so I need to find 12 one dimensional first order equations that describe the position and velocity of both masses in 3 dimensions. The equations for the second body will be easy once I figure out how to do the first body, so I'll ignore that for now. For the first equation, I can rearrange...

So really i am just unsure how to answer the last part of the question. I am unsure how to apply the low and high temperature limits the way i have done it. Do i set upper/lower limits on the integral and solve? If so i am not sure what to put Here is what he book has for 3d

We have the potential $$V(x)=-\frac{1}{\cosh^2 (x)}$$ Show that the Schrödinger equation has the solution $$\psi(x)=(\tanh(x)-ik)e^{ikx}$$ and calculate the transmission and reflection coefficients for the scattering process. It is easy to show that the given wavefunction indeed solves the...

For the given problem, I know that the quantized energy for the particles in a 1D box is given by - E(n) = n^2 h^2/ (8mL^2) Here m = mass of electron L = Length of the box = a Now, since there are 8 electrons, but only 2 can occupy one energy level, so I used n^2 = (1)^2 + (2)^2 = 1 + 4 = 5...

Hey everyone, I'm currently working on a 1D Poisson Solver for a MOS device (Al-Si-SiO2). Therefore, I programmed a Poisson Solver which is appling a boxintegration (Finite Volume Method) through the structure from φ(0) at the metal-oxide interface and φ(x_bulk = 20 nm) in in the silicon bulk...

Imagine this question in 2 dimensions, time (t) and distance (x), that is (t,x). Alice (A) is at the origin, x=0. Bob (B) begins at x=c. Thus we have A(0,0) and B(0,c). Both Alice and Bob send a light signal towards the other but let's say the signal changes colour every second by the colours of...

At the point where we 'guess' a solution to this 2nd order ODE that cannot be done analytically, I was wondering why Griff and others choose $$e^{-x^2 / 2}$$ rather than just $$e^{-x^2}$$ I've plotted both here and am left wondering what's so different? If we guessed instead the unpopular...

hi guys our solid state professor sent us a work sheet that included this example : i solved it not sure its correct tho : is it that simple , or this is not the right approach for it ?

Hi there! This is my first post here - glad to be involved with what seems like a great community! I'm trying to understand the acoustics of a finite plane-wave tube terminated by arbitrary impedances at both ends. So far all of the treatments I've managed seem only to address a different...

This is a very simple topology question. Consider two infinite lines crossing at one point. Now, I know that this is not a 1D manifold, and I know the usual argument (in the neighbourhood of the intersection, we don't have a a line, or that if we remove the intersection point, we end up with...

This is not really homework, but I'm having trouble understanding it intuitively. I came across this when learning about the space charge layer of a diode. The solution I know simply uses the 1D form of Gauss's law: ##\vec{\nabla} \cdot \vec{E}## = ##\dfrac{\rho}{\epsilon_0}## becomes...

import matplotlibimport matplotlib.pyplot as plt import numpy as np from sklearn import datasets, linear_model import pandas as pd # Load CSV and columns df = pd.read_csv("C:\Housing.csv") Y = df['price'] X = df['lotsize'] # Split the data into training/testing sets X_train = X[:-250] X_test =...

I need help with part d of this problem. I believe I completed the rest correctly, but am including them for context (a)Show that the hermitian conjugate of the hermitian conjugate of any operator ##\hat A## is itself, i.e. ##(\hat A^\dagger)^\dagger## (b)Consider an arbitrary operator ##\hat...

My teacher wants me to know how to solve for missing values in a 1D collision when v2 does NOT equal 0. Could someone do me a huge favour and make me a practice question to solve for a missing value when v2 does not equal 0? Or even point one out to me online? And then let me try it out and...

0.25g converts into 2.45m/s^2 V(t)=Vo+AoT 1=0+2.45T T=1/2.45 T=0.4s X(t)=VoT+1/2AoT X(t)=100+0+1/2(2.45)(0.4)^2 X(t)=100.196m I don't know if this is the right methodology or how to move on from here

array_values = [[0], [0,0], [1,2], [3,1,2], [1,2,3], [4,6,2,1], [8,9,0,2,1]] def peakfinder(xarray): if len(xarray) == 0: print("You entered an empty error !") raise ValueError if len(xarray) == 1: return xarray[0] if len(xarray) == 2: return...

I came across an example of a solution to finding the potential of a charged layer using the Green function (here, pdf). The standard algorithm for finding the Green function by boundary conditions for many problems is understandable: \begin{align*} G_\mathrm{Left} = Ax+ B \\ G_\mathrm{Right} =...

Hi all, I'm having a problem understanding a step in an arxiv paper (https://arxiv.org/pdf/0808.3566.pdf) and would like a bit of help. In equation (29) the authors have $$R = \frac{\sigma}{\sqrt{\pi}} \int dk \ e^{-(k - k_0)^2 \sigma^2} \ \Big( \frac{ k - \kappa}{ k+ \kappa} \Big)^2$$ where...

$$\frac{\partial T}{\partial t}=\alpha\frac{\partial^2 T}{\partial^2 t}$$ with an initial condition and boundary conditions $$T(x,0)=T_0$$ $$T(L,t)=T_0$$ $$-k\left.\frac{\partial T}{\partial x}\right|_{x=0}=2A\cos^2\left(\frac{\omega t}{2}\right)=A(\cos\omega t+1)$$ where $A=V_0^2/(8RhL)$...

Homework Statement I am solving a kinematic problem, where I have a link that is attached to a rotational joint. I need to find the position of the joint for t=0..8, and I need to do it for every 0.01s. The problem comes from the fact that I have three stages for the velocity, during t = 0..0.1...

I've been studying the 1D schrodinger equation, and getting a feel for solutions in the harmonic oscillator, or potentials of inverse radius (atomic/hydrogen), and many versions of stair-step/ square potentials (square wells.) But, I've noticed that there are very few exact 1D potentials in the...

I have got a simple qstion. We have a particle in 1d oscillator with E0( fundamental level).We know that phi~ e^-x^2 for any x, so We can measure a position and get a value x=a, such that V(a)>E0 . In this case T<0 so the velocity of the particle is imaginary, how is this even possible?, (a real...