One dimensional Definition and 145 Threads

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. S

    One dimensional harmonic oscillator

    Homework Statement One dimensional harmonic oscillator is at the beginning in state with wavefunction ##\psi (x,0)=Aexp(-\frac{(x-x_0)^2}{2a^2})exp(\frac{ip_0x}{\hbar })##. What is the expected value of full energy? Homework Equations ##<E>=<\psi ^{*}|H|\psi >=\sum \left | C_n \right |^2E_n##...
  2. Z

    One dimensional transducer data

    I posted this in Introductory Physics but not sure if that was right so I have posted here as well hope that's ok. Homework Statement To run a one dimensional transducer modelling program and analyse the data. The attempt at a solution I have ran the modelling program for different...
  3. Z

    One dimensional transducer data

    Homework Statement To run a one dimensional transducer modelling program and analyse the data. The Attempt at a Solution I have ran the modelling program for different scenarios, first the transducer itself, then with a layer of water on one side, then with a matching layer between the...
  4. C

    One Dimensional Collisions: Analyzing Impulse and Average Forces

    Homework Statement a ball of mass 2.50kg is thrown upward. it leaves the hand w/ an upward velocity of 19.6m/s. (on the way down now )after the ball hits the throwers hand it comes to rest in .20s a. What is the impulse exerted on the ball? b. What is the average net force on the ball...
  5. D

    Many Particle in a one dimensional box

    Hi pf, I am just wondering how would the system be if i keep say 5 particles in a 1-D box. How would the wave functions be? Will quantum superposition happen? Entanglement? What about the energy levels? How would they be quantized? In short i want to know how would you solve the...
  6. E

    Is it possible one dimensional plane?

    I have heard about two or above dimensional plane which we can express R2 or Rn. But I never heard about one-dimensional plane which we can express R. Is it possible one dimensional plane?
  7. D

    The net force and centre of gravity of a one dimensional object

    I have been trying to derive a formula for the forces acting on and the centre of gravity of objects in a one dimensional space. I've started in one dimension to make things easier and intend to move on to two dimensions soon. I tried to do it without referring to any source and I got a solution...
  8. W

    Electron in one dimensional infinite square well

    An electron in the ground state of a one-dimensional infinite square well of width 1.10 nm is illuminated with light of wavelength 600 nm. Into which quantum state is the electron excited? ok so I first calculated the engery of the electron in the first ground state of the square well...
  9. P

    Why is the concept of a one dimensional box used?

    I'm not sure I know all that I should to understand it. I'm posting to try and determine if I do. Knowing what I know, however, it seems unnecessarily confusing. Almost all students I talk to agree. Why not just call it a particle on a line segment? Or just moving in one dimension?
  10. Roodles01

    Normalizing: One dimensional wave function

    Homework Statement At time t = 0 a particle is described by the 1D wave function ψ(x,0) = (2α)^1/4 e^-ikx-α Verify that this is normalizedHomework Equations Er! I have just started this sort of thing, so just a bit confused. I think I can do this if there are limits as to where the particle is...
  11. O

    Understanding the One Dimensional Wave Equation

    Homework Statement Given that the the One Dimensional wave equation is \frac{∂^{2}y(x,t)}{∂x^{2}} = \frac{1}{v^{2}} \frac{∂^{2}y(x,t)}{∂t^{2}} is y(x,t) = ln(b(x-vt)) a solution to the One Dimensional wave equation? Homework Equations Shown above. The Attempt at a Solution So my Professor...
  12. A

    One dimensional Schroedinger equation solution

    Homework Statement before a potential barrier show; ψ(x) = B*sin(kx-∅) B, k and ∅ are all possitive Is a solution of the one dimensional Schroedinger equation Homework Equations ψ(x) = B*sin(kx-∅) Eψ(x) = -(ħ2/2m)(d2ψ(x)/dx2)+U(x)ψ(x)The Attempt at a Solution If it is before the barrier U(x) =...
  13. S

    Why Is the Wave Equation Dimensionally Incorrect?

    Alright so I'm clueless. I've read the chapter and the concept of a one dimensional box is never mentioned before this problem. I'm thinking i have to integrate some stuff but i have no idea where to begin. Any help?
  14. F

    One dimensional spring chain and density of states

    I have a classic infinite, linear chain of atoms, each of mass m, each separated by a spring with spring constant b and equilibrium distance a between each adjacent one. I know from my textbook that the dispersion relationship you get for this is: \Omega(k) = 2\sqrt{\frac{b}{m}} |sin(ka/2)|...
  15. B

    One Dimensional Motion Question

    Homework Statement Pelicans tuck their wings and free-fall straight down when diving for fish. Suppose a pelican starts its dive from a height of 18.0m and cannot change its path once committed. If it takes a fish 0.25s to perform evasive action, at what minimum height must it spot the pelican...
  16. K

    How far will a motorcycle travel before coming to a halt?

    1. A uniformly retarded moving motorcycle covers 250 meters in the first 10 seconds and and 250 meters in the next 20 seconds.How much will it travel more to come before coming to a halt? 250 = 10u - 50a , 250 = 20u - 200a. On solving these i get and a retardation of 2.5.
  17. J

    What is the required speed for the last 2 laps to qualify for the race?

    Homework Statement "A race car driver must average 180 km/h for 4 laps to qualify for a race. Because of engine trouble, the car averages only 150 km/h over the first 2 laps. What speed must be maintained for the last 2 laps?" Homework Equations The Attempt at a Solution So I do...
  18. R

    How can a curve be one dimensional?

    I've heard of curves being described as one dimensional but I don't understand how anything other than a straight line can be one dimensional as surely once the curve becomes, well, curved it is now in two dimensions? I have illustrated this in the above diagram with the curve and...
  19. J

    Time Dependant One Dimensional Square well

    Given the wave function: Ψtot(x,t) = ((√2)/2)ψ3e^(-(iE3t)/h) + ((√2)/2)ψ5e^(-(iE5t)/h) @ |x|≤a/2 and ψtot(x,t) = 0 @ |x|≥a/2 where a=100nm , E=(((h)^2)((kn)^2))/2m , kn=pi*n/a , & T1 = 2pih/E1 How would I find the Period of the wave function in terms of T1??
  20. S

    Schrodinger equation for one dimensional square well

    Homework Statement the question as well as the hint is shown in the 3 attachments Homework Equations The Attempt at a Solution i know how to normalize an equation, however i do not understand what the hint is saying, or how to do these integrals, any guidance would be greatly...
  21. JimiJams

    One Dimensional Collision dealing with Reference Frames

    Homework Statement A 20g ball of clay is shot to the right at 12m/s toward a 40g ball of clay at rest. The two balls of clay collide and stick together. Call this reference frame S. Homework Equations What is the velocity of a reference frame S' in which the total momentum is zero...
  22. A

    Upstream and Downstream one dimensional motion

    Homework Statement A fisherman sets out upstream on a river. His small boat, powered by an outboard motor, travels at a constant speed v in still water. The water flows at a lower constant speed vw. The fisherman has traveled upstream for 1.85 km when his ice chest falls out of the boat. He...
  23. T

    One dimensional motion- object accelerating straight downwards

    One dimensional motion-- object accelerating straight downwards Homework Statement A rocket, initially at rest, is fired at "t = 0" vertically down from a building of height "H". The rocket's acceleration, including the effects of gravity, is downwards with increasing magnitude given by a(t)...
  24. L

    What is the initial speed of the rock when thrown off a cliff?

    [b]1. When a kid drops a rock off the edge of a cliff, it take s 4.0s to reach the ground below. When he throws the rock down, it strikes the ground in 3s. What inital speed did he give the rock? ΔX=ViTf + 1/2ATf^2 H=1/2gt^2 Vf^2=Vi^2+ 2AΔX [b]3. Hi everyone! :smile: I know that when...
  25. TrickyDicky

    Riemannian surfaces as one dimensional complex manifolds

    If we consider a Riemannian surface as a one-dimensional complex manifold, what does that tell us about its intrinsic curvature? I mean for one-dimensional curves we know they only have extrinsic curvature so it depends on the embedding space, this doesn't seem to be the case for one-dimensional...
  26. Telemachus

    How Is Tension Calculated in the One Dimensional Wave Equation?

    Hi there. I was trying to understand this deduction of the one dimensional wave equation developed at the beggining of the book A first course in partial differential equations of H.F. Weinberger. You can see it right here...
  27. C

    One dimensional medium with 2 different dielectric constants

    I just got this question on a classical mechanics assignment... and unfortunately I know NOTHING about dielectric materials (never been introduced to me for some reason >.<). I don't even know why this is on my classical mechanics assignment but it is anyway. And btw there is a disclaimer on the...
  28. F

    One Dimensional Kinematics: Finding distance between two cars

    Homework Statement Car A is traveling a distance d behind Car B. Initically both cars are traveling at the same speed of 20.02 m/s. Suddenly Car B applies the brakes, causing Car B to decelerate at 3.05 m/s2. It takes the driver of Car A 0.75 seconds to react, and when she applies her brakes...
  29. C

    How Long Will It Take the Car to Catch the Truck?

    A car moving at 187km/h is behind a truck that's moving at 71km/h and is 150m ahead of the car How long will it take the car to catch the truck ? I'm literally in 2 lectures in my physics 101 class but I figure it would be cool to take a shot at the problem. This is what I did...
  30. C

    One Dimensional Motion Homework

    Homework Statement A person travels by car from one city to another with different constant speeds between pairs of cities. She drives for 45.0 min at 55.0 km/h, 17.0 min at 65 km/h, and 60.0 min at 30.0 km/h, and spends 55.0 min eating lunch and buying gas. (a) Determine the average speed...
  31. D

    One Dimensional QM particle Problem

    Dear All, This is my first post. I appreciate your help. I have the following question which i am struggling to understand, let alone solve. Consider a quantum mechanical particle with the mass m moving in one-dimensional described by the following Hamiltonian; (1)\hat{H} =...
  32. I

    When is energy quantized in a one dimensional potential.

    Homework Statement Consider a non relativistic particle moving in a 1D potential V(x). Do you consider the energy of a particle moving in this potential to be quantized? Homework Equations V(x)=A exp{alpha^2 x^2} The Attempt at a Solution I was a bit confused as I thought energy...
  33. T

    What is the Relationship Between Heat Energy and Temperature?

    Homework Statement Show that the heat energy per unit mass necessary to raise the temperature of a thin slice of thickness \Deltax from 0^o{} to u(x,t) is not c(x)u(x,t). but instead \int_0^uc(x,\overline{u})d\overline{u}. Homework Equations According to the text, the relationship...
  34. K

    A question in one dimensional Schroedinger Equation.

    I read something like this: since U(x)(the potential field) is a real,ψ and ψ* can both be the solution of Schroedinger Equation.I cannot understand this. Anyone can give me an explanation. Thanks.
  35. Y

    Statistical Mechanics - One dimensional Polymer

    Homework Statement Consider a polymer formed by connecting N disc shaped molecules into a one dimensional chain. Each molecule can align along either its long axis (of length 2a) or short axis (of length a ). The Energy of the monomer aligned along its shorter axis is higher by e, that is the...
  36. D

    Particle in one dimensional potentional well

    I hope this is in the right place, I'm new here. Anyway, my teacher hasn't shown us an example where U is anything but infinity, Uo, or 0 and I'm completely stumped on part B for this question since U is a function of x Homework Statement A particle of mass m moves in a one-dimensional...
  37. O

    Basic one dimensional kinematics problem, need conceptual help

    Hello all, I just came across a problem that I had previously solved. A relatively simple one. What I do not understand though is why I can use the equation that I have used so many times in this particular situation. Here it is: Homework Statement A baseball pitcher throws a baseball...
  38. P

    One dimensional motion problems.

    Homework Statement Hi, Physics Forum! I have three problems. Since I am having a physics final on Tuesday, I am very nervous that I don't get these. These all concern one-dimensional motion. 1.) A plane is landing on the runway. It stops after 1100 meters, with an initial velocity of 110...
  39. G

    Dimension of Complex Vector Spaces over R?

    Homework Statement C is a 1-dim comples space. What is its dimesion when regarded a vector space over R The Attempt at a Solution if the complex vector space is dim 1 then the real part must = 0 so therefore when viewed over R the dimension must be 0 as well
  40. D

    Heat transfer (steady state, one dimensional)

    Homework Statement Find the heat flow and the interface temperatures of the given figure. Homework Equations The Attempt at a Solution Do solve it correctly? I do not know how to solve the interface temperatures in case of parallel. Can you explain to me how to solve it
  41. W

    How to determine band structure (E(k)) of a one dimensional crystal?

    Hi! I'm new to the physics forum but I've read a little bit and I'm impressed with the knowledge a lot of people have here. I've tried searching for any topic on my question without any luck. My question is simply what the algorithm is to determine the band structure for a one dimensional...
  42. C

    What Happens to Electronic Energies and Wavefunctions if C is Negative?

    Homework Statement a quantum mechanics problem - the one dimension potential function is V= C when mod(x)>a and zero elsewhere. C is a constant. question 1- it is about calculating reflection coefficient which i have done. question2- if C is negative,what will happen to the electronic...
  43. M

    One Dimensional Kinematics Problem

    Homework Statement How far has the motorcycle traveled, when it catches the ferarri? A ferrari speeding at a constant 35m/s passes a police officer at rest. 2.0 s later, the officer accelerates in pursuit at 6.5 m/s^2. How far has the motorcycle traveled, when it catches the ferarri? I know...
  44. J

    Train Physics, One dimensional Motion

    Homework Statement Two trains, each having a speed of 30 miles/hr, are headed at each other on the same straight track. A bird that can fly 60 miles/hr flies off one train when they are 60 miles apart and heads directly for the other train. On reaching the other train it flies directly...
  45. P

    One Dimensional Kinematics Question (Simple)

    Homework Statement 1. A ball is rolling along the x-axis. At t=2s it is located at x =6m, at t=4s it is at x=16m, and at t=8s it is at x=48 m. Assume Constant acceleration. a) Find its displacement from 2s to 4s. -- I put 10m b) find its average velocity from 2s to 4s.---- 5 m/s c) find its...
  46. T

    One dimensional stress,strain,deflection analysis

    hi i am an undergrad student i had an eqn like the following from which i am to find deflection,stress and strain using finite difference method EI (d4 y/dx4)-m(d2y/dt2)-P sin wt=0 P=force y=deflection w=frequency t=time i have developed a MATLAB prog for deflection how can I find stress...
  47. R

    One dimensional collision of 2 unequal masses

    Imagine two particles of uneven masses colliding at relativistic velocities. What is the final velocity of each particle after the collision (no they do not stick together). This question pertains to the relativistic treatment of a one dimensional collision. Basically I tried to derive the...
  48. M

    Will Vehicle One and Vehicle Two Collide?

    Homework Statement Vehicle one driving 30 m/s. Slow moving vehicle 155 m ahead driving 5.00 m/s. Vehicle one brakes and decelerates at -2.00 m/s2. Is there a collision? If not what's the closest they get? Homework Equations Vehicle one info: Vi= 30 m/s A= -2 m/s2 \DeltaX= 155 m...
  49. M

    One-Dimensional Box: Analyzing Butadiene's UV/VIS Spectrum

    Homework Statement consider butadiene H_2 C = CH-CH=cH_2 and assume for simplicity that \pi electrons move on a straight line (one -dimensional box) whose length l can be estimated as equal to two C=C bond lengths (2*1.35 angstrom) , plus one C-C lengths. Butadiene has four \pi...
  50. Z

    Solving One Dimensional Wave Motion with Mass m

    Homework Statement A particle of mass m moves in one dimension subject to the potential energy given by: U(x) = -Uoe-(x/l)2 where Uo is a positive constant with units of energy. Supposing that at time t=0 the mass has zero velocity and is located at position 0.01l, what is the...
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