# 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.

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1. ### I Work Done/Energy Transferred in One Dimensional Collision

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...
2. ### Kinematics and One Dimensional Motion

Would we assume that the deceleration of both instance are the same?
3. ### A Conductance of an interacting quasi one dimensional wire

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...
4. ### I How Does Finite Size Scaling Reveal Cluster Behavior in 1D Percolation?

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...
5. ### Gross Pitaevskii one dimensional solution

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?
6. ### A How are the equations of continuity derived in 1D?

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...
7. ### Partition Function for Spin-1 One Dimensional Ising Model

$$H=-J\sum_{i=1}^{N-1}\sigma_i\sigma_{i+1}$$ 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) $$Z=e^{-\beta H}$$...
8. ### I A one dimensional example of divergence: Mystery

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...
9. ### One dimensional elastic collision

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...
10. ### Map a one dimensional random walk to a two-state paramagnet

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...
11. ### I One-Dimensional System: Boundary Condition Applicability

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?
12. ### I Lorentz Transformation in One-Dimensional Space

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)...
13. ### I One dimensional wave, function of a wave

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 -...
14. ### Fermi temperature of a 1D electron gas

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...
15. ### Poisson's equation in 1D with point source

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...
16. M

### How does one dimensional light warp multiple dimensions?

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?
17. C

### Acceleration in One Dimensional Inelastic Collision

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...
18. ### Probability Density in an infinite 1D square well

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...
19. ### Simple constant acceleration/equation of motion question

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...
20. ### Calculating Acceleration from Velocity and Distance: A Two-Part Problem

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...
21. ### Electron confined in a one dimensional box

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)...
22. ### I Genus of one dimensional curves

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...
23. ### One dimensional integration that Mathematica cannot do

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...
24. ### One dimensional Elastic collision of two identical particle

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...
25. ### Coefficient of restitution in different frames of references

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...
26. ### Energy eigenstates of a particle in a one dimensional box.

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...
27. ### Is the One Dimensional Wave Equation Applicable to a String Oscillating in Time?

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...
28. ### How can strings be only one dimensional?

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?
29. ### Applying Relative Motion to One Dimensional Motion Equations

<<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...
30. ### One dimensional inelastic collision; bullet through block.

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...
31. ### Why is the bi-linear bracket operation on a one-dimensional Lie algebra abelian?

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?
32. ### Thermal Ckt Parallel Configuration & 1-D HeatFlow Contradictory?

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...
33. ### A particle of mass m moves in a one dimensional potential

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...
34. ### Kinematics One Dimensional help

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...
35. ### One dimensional Kinematics help

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...
36. ### Scalar as one dimensional representation of SO(3)

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...
37. ### How Do You Calculate the Constant in a Helicopter's Takeoff Equation?

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...
38. ### Electron in a One Dimensional Infinite Potential Well

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...
39. ### QM - free particle in one dimensional dpace

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##...
40. ### Application of one dimensional force - Dynamics

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...
41. ### How Does the One-Dimensional Wave Equation Model Tensile Forces in a String?

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/...
42. ### One dimensional potential well

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...
43. ### One dimensional potential function

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...
44. ### One Dimensional motion of particle in a potential field

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...
45. ### Advanced One Dimensional Kinematic Problem

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...
46. ### Numerical solution of one dimensional Schrodinger equation

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...
47. ### One Dimensional Slab Heat Transfer Taylor Expansion in Glasstone

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?
48. ### One dimensional problems. More particles.

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...
49. ### One dimensional diatomic lattice oscillations

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
50. ### One dimensional Coulomb potential

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...