Free particle Definition and 145 Threads

Hi. I am working through a QFT book and it gives the relativistic Lagrangian for a free particle as L = -mc2/γ. This doesn't seem consistent with the classical equation L = T - V as it gives a negative kinetic energy ? If L = T - V doesn't apply relativistically then why does the Hamiltonian H =...

I am following the math of scattering theory in Sakurai, Revised Edition pp.380-381 For a free particle, one can find that the solution is a plane wave that can be written (in position space) as, <x|\phi>=\frac{e^{ip \cdot x}}{(2 \pi \hbar)^{3/2}} However, how does one obtain ##<x|p>?## In...

free particle can be thought of as unbound particle:confused: and what about square well potential with finite walls? coz it has both bound and unbound states please help m confused thanks in advance

Homework Statement A particle with mass m can move freely in three dimensions. Explain why the stationary states of the particle are determinate states for angular momentum (L_z and L^2) Homework Equations L^2 = L_x^2 + L_y^2 + L_z^2 L = r \times p \hat{H} =...

Hi, I was studying the solution of Schrodinger equation with no potential and found that the wave function is just a single plane wave eikx for movement of the particle in positive x direction. But when the phase velocity of a single wave is calculated it turns out to be less than the...

This type of integration is a special case of something that occurs over and over in QM and QFT (it's everywhere in Peskin and Schroeder), but I am having a bit of trouble working out the details. Set \hbar=1 and consider the propagation amplitude for a free, nonrelativistic particle to move...

So the free particle wave functions are of the type: ψ(x) = Aexp(ikx) + Bexp(-ikx) (1) In a problem I am doing I am supposed to find the energy levels for a particle which is sliding on a frictionless ring and the exercise says that to do so I should use the fact that ψ(x+L)=ψ(x) (2) BUT...

In my course there's a chapter with the mathematical explanation to find the real expression and localisation of a free particle with the superposited wave function. The same is used to explain the movemement of a wave packet (which is a free particle). I've worked out almost all the math behind...

Homework Statement [/B] If L is Lagrangian for a (system of) free particle(s) and dL/dt=0, show that any twice differentiable function f(L) gives the same equations of motions. Homework Equations [/B] Euler-Lagrange equations.The Attempt at a Solution Well, after some calculation, I get...

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##...

If you solve TISE with V=0, you get a plane wave. This is not normalizable, so it's not a physically achievable state. But a linear combination does (?) I know why it does from the mathematics, a linear combination of plane waves is normalizable, but what does it really mean? A free particle is...

Homework Statement Griffiths Intro Quantum Mechanics free particle question. Normalize wave function, find Phi(k), Psi(x,t), and comment on its behavior for small and large a. The wave function given is Ae-a|x|Homework EquationsThe Attempt at a Solution I found the correct Phi(k), but for the...

Homework Statement 'Consider an inertial frame in which a free particle travels past the origin O but does not go through it. Show by direct calculation that the particle's angular momentum about O is constant.' Homework Equations \frac{d\vec{l}}{dt}=∑\vec{\tau}...

Homework Statement I'm trying to figure out how the general solution of the Schrodinger equation for a free particle when v=0 relates to anything I have learned in class...Homework Equations For Eψ=(hbar2/2m)d2ψ/dx2The Attempt at a Solution I really have no idea- what is confusing me is that ψ...

Hello everyone, I've been having trouble with the following reasoning for a while. The book I use for learning is Landau and Lifschitz vol1. When the concept of the Lagrangian is introduced in textbooks it is some abstract function of the position vector, velocity vector and time. Then they try...

Hi, I´m not sure if my way of tackling a question, probably it's a trivial problem, but it's important for me to get it right so any help will be greeted. The question is as follows: Problem: consider a particle in a one-dimensional system. The wave function ψ(x) is as follows: ψ(x)= 0...

Homework Statement Find the probability current of a free particle. Homework Equations \Psi(x,t) = Aei(kx-\frac{(hbar)k^{2}t}{2m}) J(x,t) = \frac{ihbar}{2m}(ψψ*' - ψ*ψ') The Attempt at a Solution I figured it was just take the derivative of the time dependent wave function and...

Hello, this is probably one of those shoot yourself in the foot type questions. I am going through Landau & Lifshits CM for fun. On page 7 I do not understand this step: L' = L(v'^2) = L(v^2 + 2 \vec{v} \cdot \vec{\epsilon} + \epsilon^2) where v' = v + \epsilon . He then expands the...

Homework Statement A free particle moving in one dimension is in the initial state ψ(x,0). Prove that <p> is constant in time by direct calculation (i.e., without recourse to the commutator theorem regarding constants of the motion). Homework Equations <p> = m*(d<x>/dt) ? S.E. ψ(x,0)=...

Homework Statement A free particle has the initial wave function ψ(x,0)=Ae^(-a|x|) Where A and a are positive real constants. a) Normalize ψ(x,0) Homework Equations 1= ∫|ψ|^2 dx The Attempt at a Solution I attempted to normalize using 1= ∫|ψ|^2 dx from -∞ to ∞. When...

Why the Griffiths book says : any function of x and t that depends on these variables in the special combination (x±vt) represent a wave of fixed profile, traveling in the -+x direction at speed v... I don't really get the reason why from 2 terms of wavefunction can become only one term...

I've seen that the lagrangian for a relativistic free particle is -mc \sqrt{\eta_{\mu\nu} \dot{x^{\mu}}{\dot{x\nu}} but when I construct the hamiltonian as p_{\mu} \dot{x^{\mu}} - L I seem to get zero. I am not really sure what I'm doing wrong. I find that if in the first term of...

Homework Statement Consider first a free particle (Potential energy zero everywhere). When the particle at a given time is prepared in a state ## \psi (x) ## it has <x> = 0 and <p> = 0. The particle is now prepared in ## \Psi (x, t=0) = \psi (x) e^{ikx} ## 1. Give <p> at time t=0. 2...

Homework Statement The problem is given in the attached image. I'm currently trying to work out question one.Homework Equations \phi (k) = \dfrac{1}{2 \pi} \int_{- \infty}^{ \infty} \Psi (x,0) e^{-ikx} dxThe Attempt at a Solution Okay, so the first thing I did was to normalise it, but then I...

Homework Statement Hi guys, I'm stuck at some step in a QM exercise. Here it is: Consider a free particle of mass m that moves along the x-axis (1 dimensional). Show that ##\frac{dA}{dt}=\frac{2 \hbar ^2}{m^2}\int \frac{\partial \psi}{\partial x} \frac{\partial \psi ^*}{\partial...

For a free particle stationary state, one would expect the expectation values are constants, for example, <x> (t) = 0. From its one dimensional wave function psi(x,t)= exp(ipx/h-iEt/h)/L^1/2, <x> is undefinied (or zero since x has odd parity). How does one reconcile the above with Ehrenfest's...

Homework Statement Show that the free particle lagrangian is invariant to rotations in $$\Re^{3}$$, but I assume this means invariant up to a gauge term. $$L=m/2 [\dot{R^{2}} + R^{2}\dot{θ^{2}} +R^{2}Sin^{2}(θ)\dot{\phi^{2}}$$ Homework Equations I consider an aribtrary infinitesimal...

Homework Statement Sorry if this should be in intro section. I'm not sure the math required. So I have \frac{d^2\psi}{dx^2}=-\frac{2mE}{\hbar^2}\psi I would like to see how I can get the solution that my book gives me which I know is \psi(x)=A\sin kx+B\cos kx where A and B are...

In the very first example of Feynman and Hibb's Path Integral book, they discuss a free particle with \mathcal{L} = \frac{m}{2} \dot{x}(t)^2 In calculating it's classical action, they perform a simple integral over some interval of time t_a \rightarrow t_b. S_{cl} = \frac{m}{2}...

The free particle is the particle in no potential: Hψ = Eψ with V=0 you get waves traveling in + and - direction but they are not normalizeable. So for some reason my book comes up with the idea of constructing: ψ(x,t) = ∫β(k)exp(i(kx-hk2/2m t)) dk I have no idea where this came from, so...

Homework Statement http://img853.imageshack.us/img853/2532/70224197.png Homework Equations i know schrödingher eq. and basic quantum formula The Attempt at a Solution i showed that the equality at the first question but i can not start from (a) part. how and where am i supposed to start...

Homework Statement In my physics course, we have been given 'plausibility' arguments for the solutions of the time dependent/time independent SE. However, have done a Calculus course alongside, I feel I should really derive these solutions, since I have learned about the techniques of second...

Energy-momentum conservation law forbid free particle radiates.Then does free particle possibly self interact by emiting and absorbing virtue gauge boson particles?Is there a classical static field caused by ''virtue radiation'' surrounding the particle? Is the origin of mass of fermions to...

Hi there! I have tried to apply time reversal (which makes t -> -t) to a free particle wavefunction: Exp[i(p.r-Et)/\hbar] and got: Exp[-i(p.r-Et)/\hbar] I got this by flipping the sign of p since it has a d/dt part, and flipping the t in the Et part. However I think this is wrong...

what does it mean that the energy of a free particle is not quantized, but continuous just like in classical physics? I thought energy is always quantized??

could anyone explain the free particle in Quantum mechanics? when the potential is zero

Free particle --> bound particle Homework Statement A free neutron meets a finite square well of depth V_{0}, and width 2a centered around origo. However, the probability that the neutron emits a photon when it meets the potential well, and thus decreasing its energy is proportional to...

Homework Statement This is problem 2.22 from D.J. Griffiths Introduction to Quantum Mechanics A free particle has the initial wave function: \Psi(x,0)=Ae^{-ax^{2}} Find \Psi(x,t). Hint Integrals of the form: \int_{-\infty}^{\infty}e^{-(ax^{2}+bx)}dx can be handled by completing the square...

I think I'm trying to reconcile quantum mechanics and special relativity . . . or whatever I'm doing I'm pretty confused. Ok, so the allowed energy states for a particle in a box are E_n = \frac{\hbar^2 \pi^2}{2 m L^2} n^2 . This seems to mean, as you increase the length L, the particle's...

I've heard it said that the Lagrangian of a free particle cannot possibly be a function of any position coordinate, or individual velocity component, but it is a function of the total magnitude of velocity. Why is this the case? I'd be grateful for any pointers in the direction of either a...

Homework Statement At time t=0 free particle is found in state psi=const*sin(3x)*exp[i(5y+z)]. What values for energy and for momentum we can get if we measure them at t=0 and with what probability? Homework Equations Well, we know that eigenvalues of energy and momentum operator for...

Assume we have a particle lying in the xy-plane with an initial velocity in the x-direction. If an external, constant and uniform magnetic field is applied in the z-direction, the particle, assuming it has a positive charge, will begin to do circular clockwise laps. However, it seems to me...

In Landau's Mechanics, if an inertial frame \textit{K} is moving with an infinitesimal velocity \textbf{ε} relative to another inertial frame \textit{K'}, then \textbf{v}'=\textbf{v}+\textbf{ε}. Since the equations of motion must have the same form in every frame, the Lagrangian L(v^2) must be...

I read somewhere that a single particle traveling freely (not in a box, no PE function, etc.) cannot have a sharp energy. Is this correct? If so, why? As always, thanks in advance.

Homework Statement Consider the time-dependent one-dimensional Schroedinger Equation for the free particle, i.e. let the Potential be V(x)=0. Consider a wave packet, i.e. \psi(x,t)=\int_{-\infty}^{\infty}=A(k)\exp[i(kx-\omega(k)t]dk. Consider especially the Amplitude distribution...

Homework Statement Revered members, A free particle is one which has no forces acting on it and since there is no forces acting on it, so there is no potential energy and E is entirely kinetic. Homework Equations The Attempt at a Solution My doubt is, when no forces act on a...

What should we use to express free particle in Quantum Mechanics? Wave packet or plane wave? Can free particle be localized in Quantum Mechanics?

Can anyone explain to me why we use the periodic boundary condition Ψ(x)=Ψ(x+L), in order to normalize the free particle's quantum state?? I've made 2 threads already on this some time ago, but haven't got an answer still.. I hope this time i`ll have because I am really curious about the...

I am a beginner to quantum mechanics and am trying to make sense of Schrodinger's Equation. I am attempting to find probabilities in the case of a free particle in the general case. It is my understanding that the solution to Schrodinger's Equation in the general case of a free particle is as...

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...