What is Free particle: Definition and 147 Discussions

In physics, a free particle is a particle that, in some sense, is not bound by an external force, or equivalently not in a region where its potential energy varies. In classical physics, this means the particle is present in a "field-free" space. In quantum mechanics, it means the particle is in a region of uniform potential, usually set to zero in the region of interest since the potential can be arbitrarily set to zero at any point in space.

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  1. JK423

    Counting the states of a free particle (Periodic boundary conditions)

    Say you have a free particle, non relativistic, and you want to calculate the density of states (number of states with energy E-E+dE). In doing that, textbooks apply periodic boundary conditions (PBC) in a box of length L, and they get L to infinity, and in this way the states become countable...
  2. T

    Free particle - Eigenstates expansion

    Hi everybody! Two question for you: 1) Take a free particle, moving in the x direction. Its (time indipendent) wave function, in terms of the momentum is \psi(x)=\frac{e^{i\frac{p}{\hbar}x}}{\sqrt{2\pi\hbar}}. Now, i know the momentum of the particle: p. So i should not know anything about its...
  3. M

    Free particle in quantum mechanics, Dirac formalism

    The problem is very easy, maybe just something about eigenvectors that I'm missing. Go to the first two pages of the 5th chapter of ''Principles of Quantum Mechanics'', by Shankar, 2nd edition. Homework Statement Shankar wants to find the solution for a free particle in Quantum Mechanics...
  4. M

    Equations of motion por a free particle in curved spacetime

    Hi there, Physics lovers! I've got some questions for you! Denoting by (1) ds^{2}=g_{\mu\nu}dx^{\mu}dx^{\nu}=c^{2}d\tau^{2} the interval (and \tau the proper time) and using the signature (+---), we have that the equations of motion for a free particle are: (2)...
  5. M

    Deriving Stationary State Wave Functions for a Free Particle on a Ring

    Hi everyone. I want to derive for fun the stationary state wave functions for FREE a particle of mass m on a ring of radius R. The question seems trivial, but I am getting hung up on something silly. What I think I know: Since \psi can be written as a function of the radial angle \phi ...
  6. F

    Quantum Free Particle question

    Homework Statement http://img168.imageshack.us/img168/6892/img002pd.jpg this is the first half of a test we had last friday. Homework Equations \phi(k) = \frac{1}{2\pi}\int\Psi(x,0)e^{-ikx}dx that looks a little funky but i think you understand what I am trying to say. The...
  7. C

    Free particle in Minkowski spacetime

    Homework Statement A free particle is moving in the x direction through Minkowski spacetime, and has velocity V as measured by a stationary observer at x = 0; t = 0. Express the particle's world-line parametrically in terms of V , parametrized by the particle's proper time  Homework...
  8. S

    Uncertainty principle free particle

    Show that for a free particle the uncertainty relation can be written as (Delta lambda) (Delta x) >= lambda^2 / 4pi Firstly I am sorry not writing this in latex but I gave up after trying to write it in latex for half an hour. Would be great if anyone can show me how to do it. Using...
  9. A

    Why Can't Free-Particle Wave Functions Be Normalized Over Their Entire Range?

    why it is not possible to normalize the free-particle wawe functions over the whole range of motion of the particles?
  10. B

    Propagator for a free particle / schrodinger equation

    http://img18.imageshack.us/img18/4295/eqn.png here is the text preceding the exercise: http://yfrog.com/5mch5p in the exercise, where does the factor \frac{m}{(2mE)^{1/2}} come from? Comparing that equation with 5.19 (bottom right of link), why can't we just replace |p> with |E,+> and |E,->...
  11. E

    Understanding the Lagrangian of a Free Particle?

    Hello, I'm trying to follow an argument in Landau's Mechanics. The argument concerns finding the Lagrangian of a free particle moving with velocity v relative to an inertial frame K. (of course L=1/2 mv^2, which is what we have to find). I'll state the points of the argument: (0) It has...
  12. sweet springs

    Is energy of a free particle observable?

    Is Hamiltonian of a particle in free space H=P^2/2m OBSERVABLE ? -Yes, we can surely observe energy in some manner. -No, ∫de|e><e| is not identical operator I, thus |e>s does not form a complete set. As an example, energy eigenstate |e> degenerates, as |e=p^2/2m> = α|p> + β|-p>, according to...
  13. Q

    Rewriting the propagator for the free particle as integral over E

    Homework Statement (This is all with respect to a free particle) Show that the propagator U(t) = \int_{-\infty}^{\infty} |p><p| exp\left(\frac{-i E(p) t}{\hbar}\right) dp can be rewritten as an integral over E and sum over the \pm index as: U(t) = \sum_{\alpha = \pm}...
  14. S

    Expressions for \gamma and \theta in terms of \alpha and \beta?

    Homework Statement For a free particle, i have two expressions. \varphi(x) = \alphaeikx + \betae-ikx and \varphi(x) = \gammasin(kx) + \thetacos(kx) I have to determine expressions for \gamma and \theta in terms of \alpha and \beta. Homework Equations sin(kx) = (eikx -...
  15. E

    Normalizing Free Particle Homework: \psi(x,t)

    Homework Statement \psi(x,0)=Ae^{-ax^2} Normalize and find: \psi(x,t)Homework Equations 1=\int_{-\infty}^\infty\psi^*\psi dxThe Attempt at a Solution 1=A^2\int_{-\infty}^\infty e^{-2ax^2} dx let: u=x\sqrt{2a} 1=A^2\frac{1}{\sqrt{2a}}\int_{-\infty}^\inftye^{-u^2} du=A^2\sqrt{\frac{\pi}{2a}}...
  16. E

    Free particle in spherical box

    Homework Statement Hello everybody: I have a problem with the Schrödinger equation in 3D in spherical coordinates, since I'm trying to calculate the discrete set of possible energies of a particle inside a spherical box of radius "a" where inside the sphere the potential energy is zero...
  17. Q

    The Lagrangian for a free particle

    According to Landau textbook: Having two inertial frames K and K' moving with velocities \vec{v} and \vec{v'}=\vec{v} + \vec{\epsilon} where \vec{\epsilon} is an infinitesimal. We have L' = L(v'^2) = L (v^2 + 2 \vec{v} \cdot \vec{\epsilon} + \epsilon^2). Expanding this expression in powers of...
  18. X

    Does a Free Particle in Quantum Mechanics Have Constant Energy?

    Hi, I'm new to QM (and phy forum :D), and studyin alone..! so, if you consider the free particle, it does not have a solution in the form of separable solutions(??). Which means that if the same experiment (independent, of course,) is carried out total energy is different each time at t = ta...
  19. C

    Free particle in spherical polar coords

    Homework Statement Consider the time-independent Schrodinger equation in spherical polar coordinates for a free particle, in the case where we have an azimuthal quantum number l=0. (a) Solve the radial equation to find the (unnormalized) radial wavefunction R(r). (b) Normalize R(r), using...
  20. T

    Schrodinger equation of a free particle in the rectilinear

    Schrodinger equation of a free particle in the rectilinear With the wave function in the laboratory reference already known, relate the wave functions of the initial and new references via phase factors, and represent the time and spatial derivatives of the initial wave function with those...
  21. T

    Momentum operator for a free particle with a definite momentum and Energy

    Hi! I need an explanation: Is the momentum operator for a free particle with a definite momentum and energy the same as what we know as the momentum operator in general? Is it just -ih/2PI()*partial/partial_x? With the justification that since the momentum is definite, delta p is 0...
  22. I

    Fourier transform for a localized free particle

    Homework Statement This is from Griffiths Introduction to Quantum Mechanics, Problem 2.21. Suppose a free particle, which is initially localized in the range -a<x<a, is released at time t=0: \Psi(x,0) = \begin{cases} \frac{1}{\sqrt{2a}}, & \text{if } -a<x<a,\\ 0, &...
  23. K

    Can Fourier Transformation be Used for Amplitude of a Free Particle?

    I hope this is the correct place for my question. I posted it here, because it`s from Peskin & Schroeder: "Consider the amplitude for a free particle to propagate from \mathbf{x}_{0} to \mathbf{x} : U(t)=\left\langle \mathbf{x}\right|e^{-iHt}\left|\mathbf{x_{0}}\right\rangle In...
  24. K

    Free particle and Heisenburg uncertainty principle

    Homework Statement Assuming at time is zero, the wavefunction of a free particle is given as \Psi(x, 0) = \left\{ \begin{matrix} 0, \quad x<0\\ f(x), \quad x>0 \end{matrix} \right. where f(x) is integrable within (0, \infty) Find the time evolution of \Psi(x, 0). Write down...
  25. N

    Free particle at time t

    Homework Statement a free particle of mass m moving in one dimension is known to be in the initial state ψ(x,0)=sin(k_0 x) 1. what value of p (momentum) will measurement yield at the time t,and with what probabilities will these values occur? 2. suppose that p is measurement at t=3 s and the...
  26. G

    Proving Dirac Theory: Free Particle Acceleration

    Homework Statement Hi all, how i can prove that in dirac theory free particle possesses acceleration. Homework Equations The Attempt at a Solution Did not find anywhere.
  27. L

    QM Free Particle Approaching Infinite Barrier

    Solved... i think. It's just Psi(x) = B sin kx Homework Statement Consider a free particle psi(x) = A*e^(ikx) approaching an infinite barrier from the left: V = 0, x < 0 and V = oo, x >= 0. For this problem use only the time-independent Schrodinger Equation. a. Find the probability of being...
  28. N

    Should we think a free particle as a particle in an infinitely big box?

    I've found that the momentum expectation of a particle inside an one dimensional finite box of length 'L' is '0'... we can say the probability of going right=that of the left... so sum up to zero. Now I calculate the same(<p>) for a free particle in one dimension if I think that free particle is...
  29. D

    Free Particle Mass m: Probability and Wavefunction Solutions

    Problem A free particle of mass m moving in one dimension is known to be in the initial state \psi(x, 0) = \sin(k_0 x) a) What is \psi(x, t)? b) What value of p will measurement yield at the time t, and with what probabilities will these values occur? c) Suppose that p is measured at...
  30. D

    Free particle in One Dimension

    Problem Consider a free particle moving in one dimension. The state functions for this particle are all elements of L^2. Show that the expectation of the momentum \langle p_x \rangle vanishes in any state that is purely real. Does this property hold for \langle H \rangle? Does it hold for...
  31. R

    Why Must the Term dL/d(v^2) v.e Be Linear in v to Be a Total Time Derivative?

    In section 4 of Landau and Lifgarbagez they derive the expression for the kinetic energy by expanding the Lagrangian around v+e. The resulting expression has a term which must be a total time derivative so that the equations of motion are unaffected. The text claims that the term dL/d(v^2) v.e...
  32. I

    Wavefunction of relativistic free particle

    Could anyone please help with the following, rather unusual, query? I know that for spin 0 bosons, the Klein Gordon equation gives solutions that are similar to the solutions of the Schrodinger equation for a non-relativistic free particle, the only difference being that the energy used when...
  33. M

    Quantum mechanics - a free particle

    Hello everyone! If we measure the position of a particle in a free space, and say we find that it is at x0, what is the wavefunction right after the measurement in x representation? shouldn't it be delta (x-x0), because delta functions are the eigenfunctions of the position operator...
  34. S

    Probability Current for Free Particle Wave Function

    [SOLVED] Probability Current for Free Particle Wave Function Homework Statement Find the probability current, J for the free particle wave function. Which direction does the probability current flow?Homework Equations J(x,t) = \frac{ih}{4\pi m}\left(\Psi \frac{\partial \Psi^{*}}{\partial x} -...
  35. C

    Physical meaning of the 2 eigenfunctions of Free Particle

    For Schrodinger's equation \frac{\d^2\psi}{dx^2} = - \frac{2mE}{\hbar^2}\psi Solving to find that \psi = Aexp(ikx)+Bexp(-ikx) I am curious about the physical meanings of the two terms of the solutions. In solving a free particle encountering a potential barrier, In the...
  36. N

    How can the momentum be non-zero if the probability current density is zero?

    I am reading One-dimensional examples from Bransden and Joachain.For the free particle solutions:Ψ=A exp [i(kx-ωt)] +B exp [–i(kx+ωt)] they say that for |A|=|B|,the probability current density=0.This is OK.Then they say we can associate the standing wave with a free particle along the x-axis...
  37. P

    Free particle with Coulomb Perturbation

    Homework Statement This is a question I have about something stated in a textbook without much explanation. From Richard D. Mattuck's "A guide to Feynman Diagrams in the Many-Body Problem" Appendix A.1 pg 337 "for example consider the Coulomb interaction between two electrons in a metal...
  38. E

    How does one develop a Hamiltonian for a free particle?

    The equation for the Hamiltonian is H = T + V. Can someone explain how you can use this to get this equation for a free particle: i\hbar|\psi'> = H|\psi> = P^2/(2m)|\psi> The first part is obviously Schrodinger's equation but how do you get H = P^2/2m? Go to page 151 at the site below...
  39. G

    Solving Free Particle Action with Feynman & Gibbs

    I've recently started Feynman & Gibbs. I was sure exercises will be fun, but i can't enjoy myself when i fail solving the first one! Exercise 1-1 says: show that free particle action is \frac{m}{2} \frac{x_b^2 - x_a^2}{t_b-t_a} I tried finding anti-derivative of \dot x^2, ended up with...
  40. M

    Normalizing the wave function of a free particle

    Hello! Can somebody tell me, how it is possible to normalize the wave function of a free particle using the Dirac delta function? Thanks!
  41. M

    Stationary states of free particle

    The problem is to obtain the stationary states for a free particle in three dimensions by separating the variables in Schrödinger's equation. So take \psi(\mathbf{r},t) = \psi_1(x) \psi_2(y) \psi_3(z) \phi(t) and substitute it into the time-dependent Schrödinger equation. For the...
  42. E

    Relativistic Lagrangian of a Free Particle

    Hi, As argued in Jackson p. 580, the quantity \gamma L is invariant. So imagine a free particle. In the particle's frame, the particle can be treated non-relativistically since its v << c (it's zero). But non-relativistically we define the L = T - V . In the particle's frame, this...
  43. S

    Free particle wave equation

    for a free particle, the wave equation is a superposition of plane waves, \psi(x,0)= \int_{-\infty}^{\infty}g(k)\exp(ikx)dk and g(k)= \int_{-\infty}^{\infty}\psi(0,0)\exp(-ikx)dx one is the Fourier transform of the other. some cases to solve this is when we assume a small delta k, so...
  44. F

    Wave function of a free particle

    A short question: I've learned that the wave function corresponding to a free particle has this form: Psi(x,0)=1/sqrt(2*Pi)*Integral[g(k)*E^(ikx)dx] (i can't write it in Latex, sorry) Is it just for the free particle, or any quantum state of a system can be represented in this form...
  45. M

    No free particle in real world

    maybe it is an easy question but i confuse a bit wave func of free particle is A exp(ikx) and probability over all space is A^2 so it is possible to find this particle everywhere Does it mean "there exist no free particle in real world" ?
  46. B

    Solution to Free Particle Schrödinger Equation: Unnormalizable?

    One solution to the time-independent Schrödinger equation for a free particle (moving in 1 dimension) is: \psi(x) = Ae^{ikx} This has a definite momentum p = h-bar*k, but it can't be normalized since: \int_{-\infty}^{\infty}\lvert\psi(x)\rvert^2dx = \int_{-\infty}^{\infty}|A|^2dx =...
  47. A

    Exploring the Energy and Absorption Spectrum of Free Particles in Plasmas

    Hi, this is a silly question Energy of a free particle is not quantized. Does it mean that it should have a continuous absorption spectrum?. When a cloud of free electrons in some type of plasmas is irradiated with light, theese "hot electrons" are accelerated as they absorb light. So...
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