What is One dimensional: Definition and 145 Discussions
In physics and mathematics, a sequence of n numbers can specify a location in n-dimensional space. When n = 1, the set of all such locations is called a one-dimensional space. An example of a one-dimensional space is the number line, where the position of each point on it can be described by a single number.In algebraic geometry there are several structures that are technically one-dimensional spaces but referred to in other terms. A field k is a one-dimensional vector space over itself. Similarly, the projective line over k is a one-dimensional space. In particular, if k = ℂ, the complex numbers, then the complex projective line P1(ℂ) is one-dimensional with respect to ℂ, even though it is also known as the Riemann sphere.
More generally, a ring is a length-one module over itself. Similarly, the projective line over a ring is a one-dimensional space over the ring. In case the ring is an algebra over a field, these spaces are one-dimensional with respect to the algebra, even if the algebra is of higher dimensionality.
I spend a lot of time thinking about collision problems because for me they are both extremely interesting and often very difficult to grasp when one thinks about them beyond the basics we are taught in introductory or even intermediate university courses.
Suppose there is a perfectly elastic...
Assuming the electrons are non interacting and spin degenerate, the conductance of a quasi one dimensional quantum wire is quantised in units of 2e^2/h. For small voltages, we simply count how many bands have their bottoms below the chemical potential and multiply this by 2e^2/h. This is due to...
Hello
I am struggeling with a problem, or perhaps more with understanding the problem.
I have to simulate a one dimensional percolation in Python and that part I can do. The issue is understanding the next line of the problem, which I will post here:
"For the largest cluster size S, use finite...
Hey guys, new to the forum here! I'm having this excercise where I have to prove that the solution of Gross Pitaevskii in one dimension, is equal to: φ(x)=Ctanh(x/L) for a>0 and φ(x)=C'tanh(x/L). The differential equation goes like this:
Any thoughts on what approximations do I have to use?
In Landau-Lifshitz Volume 6 Fluid-Mechanics the following problem is given Where the equation of continuity is given earlier:As is Euler's equation:And the equation of continuity for entropy:I don't understand how this conclusion was reached. I can understand the derivation for the equation of...
$$H=-J\sum_{i=1}^{N-1}\sigma_i\sigma_{i+1}$$ There is no external magnetic field, so the Hamiltonian is different than normal, and the spins $\sigma_i$ can be -1, 0, or 1. The boundary conditions are non-periodic (the chain just ends with the Nth spin)
$$Z=e^{-\beta H}$$...
I am trying to understand “divergence” by considering a one-dimensional example of the vector y defined by:
. the parabola: y = -1 + x^2
The direction of the vector y will either be to the right ( R) when y is positive or to the Left (L).
The gradient = dy/dx = Divergence = Div y = 2 x
x...
A simple model often used to explain solar system gravitational slingshots is to consider a mass moving to the right with initial velocity v1i and a much larger mass moving to the left with initial velocity v2i. After the collision, the first mass is moving to the left with velocity v1f and the...
1. The question asks us to map a one dimensional random walk to a two state paramagnet and then write an expression for the number of journeys of N steps which end up at r=Rdelta.
Then we are asked to find an expression for the probability that N steps will end up at r.
2...
In one dimensional system the boundary condition that the derivative of the wave function Ψ(x) should be continuous at every point is applicable whenever?
If space only had one dimension would Einstein's speed of light postulate still lead to Lorentz transformation for motion along that one dimension?
Relativity of simultaneity can obviously be demonstrated in one dimension (lightning bolts hitting opposite ends of stationary and moving train)...
I am currently reading through 'Optics' by Eugene Hecht chp 2 page 20, he talks about the function of the wave and the direction of travel of the wave i.e ##\psi(x)=f(x-t)## and right at the bottom of the page he say this:
Equation (2.5) is often expressed equivalently as some function of ##t -...
Homework Statement
Consider a one-dimensional metal wire with one free electron per atom and an atomic spacing of ##d##. Calculate the Fermi temperature.
Homework Equations
Energy of a particle in a box of length ##L##: ##E_n = \frac{\pi^2 \hbar^2}{2 m L^2} n^2##
1D density of states...
Homework Statement
Solve ##\Delta\phi = -q\delta(x)## on ##\mathbb{R}##.
Correct answer: ##\phi = -\frac{q}{2}|x| + Ax + B##
Homework EquationsThe Attempt at a Solution
In one dimension the equation becomes ##\frac{d^2 \phi}{d x^2} = -q\delta(x)##. We integrate from ##-\infty## to ##x## to...
If light is one dimensional, yet has gravity, and gravity is the warpage of spacetime, and spacetime has four dimensions, then how does a one dimensional wave/particle warp multiple dimensions?
Homework Statement
Two cars of 540 kg and 1400 kg collide head on while moving 80 km/h in opposite directions. After the collision, the automobiles remain locked together.
Find the velocity of the wreck, the kinetic energy of the two-automobile system before and after the collision, and find...
Homework Statement
The wave function of a particle of mass m confined in an infinite one-dimensional square well of width L = 0.23 nm, is:
ψ(x) = (2/L)1/2 sin(3πx/L) for 0 < x < L
ψ(x) = 0 everywhere else. The energy of the particle in this state is E = 63.974 eV.
1) What is the rest energy...
Homework Statement
A 747 Jumbo Jet must reach a speed of 290km/h by the end of the runway to lift off. The 15L-33R runway at Toronto International Airport is 2,770 meters long. The main Toronto Island Airport runway 08-26 is 1216 meters long. Assuming the jet has a constant acceleration, for...
So this question has two parts. The first I got without any trouble:
"Two objects move with initial velocity of -8.00 m/s, final velocity of 16.0 m/s, and constant accelerations. (a) The first object has displacement 20.0 m. Find its acceleration."
I used The formula Vf2=Vi2+2aΔx and got an...
Homework Statement
An electron confined in a one-dimensional box is observed, at different times, to have energies of 27 eV , 48 eV , and 75 eV .
What is the length of the box? Hint: Assume that the quantum numbers of these energy levels are less than 10.
Homework Equations
E=h^2n^2/(8mL^2)...
Hello,
In a physics paper, I have encountered an expression about genus of one dimensional anharmonic oscillators. More specifically, they classify cubic and quartic anharmonic oscillator as "genus one potentials" and higher order anharmonic oscillators as "higher genus potentials".
I am new...
I want to evaluate $$\int_{a+b-c}^s\,\text{d}x\, \frac{(-x+ab/c)^{\epsilon}}{(x+c-a-b)^{\epsilon+1} (a-x)},$$ where ##a,b,c,\epsilon## are numbers, and to be treated as constants in the integration. I put this into mathematica and an hour later it is still attempting to evaluate it so I aborted...
Hi everyone. I've a question that i wondered since the high school. Let's take two identical particles (same mass) that collide frontally. Assume it's an elastic collision. We have to conservate both the momentum and kinetic energy:
v_1 + v_2 = v'_1 + v'_1
v^2_1 + v^2_2 = v'^2_1 + v'^2_1...
To simplify my question I would like to use a random example (although, the issue holds regardless of the numbers you pick). Suppose two objects collide (head-on) in one dimension. The initial parameters are as follows (units are irrelevant):
m1=1;m2=2;u1=3;u2=-4;
Also, suppose that exactly...
Homework Statement
A One dimensional box contains a particle whose ground state energy is ε. It is observed that a small disturbance causes the particle to emit a photon of energy hν=8ε, after which it is stable. Just before emission a possible state of the particle in terms of energy...
Hai PF,
I had a doubt in the sector of partial differential equation using one dimensional wave equation. Actually the problems is below mentioned
:smile: A string is stretched and fastened at two points x=0 and x=2l apart. motion is strated by displacing the string in the form...
When they say strings are one dimensional, do they mean that the height and width are really small that its only the length that matters? And if not, how can a one dimensional object exist if it has no height or width?
<<Moderator note: LaTeX corrected>>
Problem:
> Two cars A and B move with velocity ##60 kmh^{-1}## and ##70 kmh^{-1}##. After a certain time, the two cars are 2.5 km apart. At that time, car B starts decelerating at the rate 20 kmh-2. How long does Car A take to catch up with Car B?
I tried to...
Homework Statement
In the figure here, a 12.8 g bullet moving directly upward at 930 m/s strikes and passes through the center of mass of a 8.3 kg block initially at rest. The bullet emerges from the block moving directly upward at 520 m/s. To what maximum height does the block then rise above...
I just read that the bi-linear bracket operation on anyone dimensional lie algebra is abelian (vanishing) because of the anti-symmetry property. I'm not understanding the connection, can anyone enlighten me?
1. My Conceptual Questions (5) is at 3.
CONSIDER:
Case 1: two dissimilar slabs of material (say slab 1 and slab 2) connected in series (bonded at their interface). There is a temperature difference: T1 @ slab1 and T2 @ slab2.
Case 2: two dissimilar slabs of material bonded together, i.e...
1.The problem, statement, all variables and given/known data
A particle of mass m moves in a one dimensional potential U(x)=A|x|3, where A is a constant. The time period depends on the total energy E according to the relation T=E-1/k
Then find the value of k.
2. Homework Equations
V=dx/dt...
Homework Statement
A train starts from a station with a constant acceleration of at = 0.40 m/s2. A passenger arrives at the track time t = 6.0s after the end of the train left the very same point. What is the slowest constant speed at which she can run and catch the train. Sketch curves for...
Homework Statement
2. An elevator ascends with an upward acceleration of 4.0 ft/s2. At the instant its upward speed is 8.0 ft/s, a loose bolt drops from the ceiling of the elevator 9.0 ft from the floor. Calculate:
a. the time of flight of the bolt from ceiling to floor.
b. the distance it has...
Hi to all the readers of the forum.
I cannot figure out the following thing.
I know that a representation of a group G on a vector spaceV s a homomorphism from G to GL(V).
I know that a scalar (in Galileian Physics) is something that is invariant under rotation.
How can I reconcile this...
Homework Statement
As a helicopter carrying a crate takes off, its vertical position (as well as the crate's) is given as: y(t)= At^3, where A is a constant and t is time with t=0 corresponding to when it leaves the ground. When the helicopter reaches a height of h = 15.0m the crate is released...
Homework Statement
An electron is confined to a narrow evacuated tube. The tube, which has length of 2m functions as a one dimensional infinite potential well.
A: What is the energy difference between the electrons ground state and the first excitied state.
B: What quantum number n would the...
Homework Statement
A particle in one dimensional space, $$H=\frac{p^2}{2m}$$ in time ##t=0## has a wavefunction $$
\psi (x)=\left\{\begin{matrix}
\sqrt{\frac{15}{8a}}(1-(\frac{2x}{a})^2) &,|x|<\frac a 2 \\
0 & , |x|>\frac a 2
\end{matrix}\right.$$
a) Calculate the expected values of ##x##...
Homework Statement
Superman must stop a 120-km/hr train in 150 m to keep it from hitting a stalled car on the tracks. If the trains mass is 3.6 x 10^5 kg, how much force must he exert?
Vi = 33 m/s (120 km/h)
Vf = 0 m/s
Displacement (Xf - Xi) = 150 m
M = 3.6 x 10^5 kg[/B]Homework Equations...
Homework Statement
Reading the very first chapter of Weinberger's First Course in PDEs, I stumbled over the derivation of the tensile force in the horizontal direction. The question was posted already in this thread: https://www.physicsforums.com/threads/one-dimensional-wave-equation.531397/...
Homework Statement
A particle of mass m is confined in a one dimensional well by a potential V. The energy eigenvalues are
E_{n}=\frac{\hbar^2n^2\pi^2}{2mL^2}
and the corresponding normalized eigenstates are
\Phi_{n}=\sqrt{\frac{2}{L}}sin(\frac{n\pi x}{L})
At time t=0 the particle is in the...
Homework Statement
A particle constrained to move in one dimension (x) is the potential field
V(x)=[(V_0(x-a)(x-b))/(x-c)^2]
(0 < a < b < c < infinity)
(a) Make a sketch of V
(b) Discuss the possible motions, forbidden domains, and turning points. Specifically, if the particle is known to...
A classical particle constrained to move in one dimension (x) is in the potential field V(x) = V0(x – a)(x –b)/(x – c)^2, 0 < a < b < c < ∞.
a. Make a sketch of V
b. Discuss the possible motions, forbidden domains, and turning points. Specifically, if the
particle...
A car is traveling at 25 m/s when it runs off the road and hits a utility pole. The car stops instantly, but the driver continues to move forward at 25 m/s. The airbag starts from rest with a constant acceleration from a distance of 50 cm away from the driver and makes contact with him in 9...
Hi,
I want to solve one dimensional Schrodinger equation for a scattering problem. The potential function is 1/ ( 1+exp(-x) ). So at -∞ it goes to 0 and at ∞ it's 1. The energy level is more than 1. I used Numerov's method and integrated it from +∞ (far enough) backwards with an initial value...
Hi There,
I came across the following passage in Sam Glasstone's 'Nuclear Reactor Engineering'
See where I underlined in red that taylor series expansion? I don't understand how (dt/dx)_(x+dx) is equal to that.
I know it's a Taylor series expansion, but where did the x+dx go?
If I have one dimensional problem with many particles that are all in same ##|\psi\rangle## state is it equal to one dimensional problem of one particle in state ##|\psi\rangle##.
If I have for example 50 particles in some state ##\psi(x)## in infinite potential well and that state is symmetric...
Suppose we allow two masses M1 and M2 in a one dimensional diatomic lattice to become equal. what happens to the frequency gap? what about in a monatomic lattice?
Knowing that (M1)(A2) + (M2)(A1) = 0
Consider the potential below:
V(x)=\left\{ \begin{array}{cc} -\frac{e^2}{4\pi\varepsilon_0 x} &x>0 \\ \infty &x\leq 0 \end{array} \right.
The time independent Schrodinger equation becomes:
\frac{d^2X}{dx^2}=-\frac{2m}{\hbar^2} (E+\frac{e^2}{4\pi\varepsilon_0 x})X
I want to find the ground...