Infinite square well Definition and 150 Threads

Homework Statement Consider a point particle of mass m contained between two impenetrable walls at +/- 2a. The potential V(x) between the walls is zero. Assume that at time t=0 the state of the particle is described by the wave function \Psi(x) = A\frac{1+cos(\frac{2*\pi*x}{a})}{2} for...

Homework Statement Find the wavefunction for an infinite well, walls are at x=0 and x=L(include the time dependence) The Attempt at a Solution I don't understand what it's meant by include the time dependence. Can I just find the time-independent wavefunction and then multiply it by...

SPECIFICALLY SEE POST 8 AND AFTER PLEASE Hi so that I can get the help for the specific problem I am working on I will set the question up and include all the steps that I can get and work out. The end question will be about quantized energy levels. This is for a maths module. I am...

Hi, I am having trouble understanding an example from a textbook I am reading on the Schrodinger equation. The example deals with an infinite square well in one dimension. With the following properties: V = 0\,where -a \leq x \leq a V = \infty\,|x| \geq a Where V is the potential. The...

Homework Statement Find the energy of a particle of mass m in an infinite square well with one end at x=-L/2 and the other at x=L/2. Homework Equations Schrodinger Equation The Attempt at a Solution To save time, I won't type the solving of the differential equation which results...

Homework Statement Griffiths Intro to Quantum, problem 2.38: A particle of mass m is in the ground state of the infinite square well. Suddenly the well expands to twice its original size: the right wall moving from a to 2a, leaving the wave function (momentarily) undisturbed. The energy of...

For the ground state of a particle moving freely in a one-dimentional box 0\leqx\leqL with rigid reflecting end-points, the uncertainty product (del x)(del p) is 1 h/2 2 sqrt{2}h 3 >h/2 4 h/sqrt{3} I used (del x)^2 =<x^2>-<x>^2 and (del p)^2 =<p^2>-<p>^2 Using the wavefunction of...

Homework Statement I'm trying to find the geometric phase for the adiabatic widening of the infinite square well. Griffiths defines the geometric phase to be: \gamma=i* \int^{w2}_{w1}<\psi_{n}|\frac{d\psi_{n}}{dR}>dR Where R is the aspect of the potential that is changing and w1, w2 are the...

Homework Statement I have infinite square well which has a potential V(x)=\frac{\hbar^2}{m}\Omega\delta(x) in x=0, and is 0 in the interval x\in[-a,a]Homework Equations Schrodinger eq.The Attempt at a Solution I solved the time independant Schrodinger eq. by integration around x=0 by some...

Homework Statement The eigenstates of the infinite square well are not energy eigenstates and are not momentum eigenstates. Homework Equations The Attempt at a Solution I don't understand how this can be? If the eigenstates of the infinite square well are energy eigenstates...

Homework Statement Pro #2 if you click on this link. http://s1104.photobucket.com/albums/h332/richard78931/?action=view&current=hw4.jpg Homework Equations , The Attempt at a Solution Click here http://s1104.photobucket.com/albums/h332/richard78931/?action=view&current=2a.jpg...

(a) Obtain the ground state wave function and energy. Draw the wave function \psi_{1}(x) (how many nodes are there in the ground state?) and the probability \left | \psi_{1}(x) \right |^{2} of finding the particle in dx about x. V(x)=\begin{cases} & \infty,\text{ }x \geq a, x\leq -a \\...

Homework Statement A particle of mass m in the infinite square well is subjected to the perturbation H'=Vo, 0<x<L/2, H'=0 else. (a) use first order perturbation theory to calculate the energies of the particle (b) what are the first order corrected wave functions? (c) if the particle is an...

Does the momentum space of a particle in an infinite square well have spikes or is it continuous? I've heard so many differing opinions on this. I go online and heaps of websites say that you just do a Fourier transform on position to get the momentum, and if you go through with this you'll...

I've been working at this problem for about an hour and can't seem to make any progress. Any help would greatly be appreciated. Homework Statement Estimate the ground state energy level of a proton in the Al nucleus which has a potential energy of 100 MeV. Compare your answer to that...

If you have 2 identical, noninteracting Fermions in an infinite 1 dimensional square well of width a, I was thinking the state would be: \frac{1}{\sqrt{2}}\psi_1(x_1)\psi_1(x_2)(\uparrow\downarrow - \downarrow\uparrow ) where \psi_1 is the ground state of the single particle well problem...

Homework Statement The question comes straight from Intro to QM by Griffiths (pg 29, Q 2.6). A wave equation is given representing an even mixture of the first two energy levels of the infinite square well. The task is to normalize the wave function, state it explicitly and then derive...

Homework Statement Calculate the 1st order probability an electron in the ground state of an infinite sqaure well (width 1) will be found in the first excited state t seconds after the pertubation H=sin(PI*x) is switched on. Homework Equations Transition frequency is omega_12 The Attempt at a...

Homework Statement The potential for an infinite square well is given by V=0 for 0<x<a and infinite elsewhere. Suppose a particle initially(t=0) has uniform probability density in the region a/4<x<3a/4 : a.) Sketch the probability density b.) Write an expression for the wavefunction...

Homework Statement We have an infinite square well potential of width 2L centered at the origin, with an attractive delta function potential V0δ(x) at the origin, with the properties V_0<0, -V_0>\frac{\hbar^2}{mL^2} Determine the conditions for a negative energy bound state. There are a few...

A particle is in the ground state of the 1D infinite square well (0<x<a). Suddenly the well expands, the right wall moving from a to 2a, leaving the wave function (momentarily) undisturbed. The energy of the particle is now measured. What is the most probable result, and what is its probability...

Homework Statement Regarding the wave function in an infinite square well extending from -L to L: If the position is measured at time t, what results can be found and with what probabilities will this results be found? Homework Equations the wave function is a superposition of the...

Homework Statement Show that E<0 solutions to the infinite square well potential are not applicable (precisely show that boundary conditions are not satisfied when E<0) Homework Equations Time independent Schrodinger equation V(x) = 0 , 0<x<a V(x) = inf otherwise The Attempt at a Solution...

Hi all, Sorry if this question is not very challenging, but I am driving myself to confusion... I happily derived the eigen functions for an infinite square well spanning from 0 to L and found them to be: ...in agreement with wikipedia. However my course notes derive solutions...

Homework Statement This problem comes from David Griffiths' quantum mechanics book which I have been going through on my own. A particle in the infinite square well has its initial wave function as an even mixture of the first two stationary states \Psi(x,0) = A(\psi_1 (x) + \psi_2 (x) I...

Homework Statement A particle of mass m is in a one-dimensional infinite square well that extends from x = –a to x = a. a) Find the energy eigenfunctions ψn (x) and corresponding eigenvalues En of this particle. (Hint: you may use the results of the book for an infinite square...

Homework Statement Twelve nucleons are in a one dimensional infinite square well of length L = 3 fm. Using a mass of 1 u. What is the ground state energy of the system of 12 nucleons in the well if all the nucleons are neutrons so that there can only be 2 in each state. Homework...

Homework Statement consider a particle of mass m in the ground state of an infinite square well potential width L/2. What is the probability of detecting the particle at x=L/4 in a range of \Deltax=0.01L (d not integrate)? Assume that the particle is in the normalized state...

Actually, this is more of a general question relating to a homework problem I already did. I was given the initial wavefunction of a particle in an infinite square well: \Psi(x,0) = Ax if (0 \leq x \leq \frac{a}{2}), and =A(a-x) if (\frac{a}{2} \leq x \leq a) And of course \Psi(0,0) =...

Homework Statement Seven electrons are trapped in a one dimensional infinite square well of length L. What is the ground state energy of this system as a multiple of h2 / 8mL2?Homework Equations Energy of a single electron in state n is n2h2 / 8mL2The Attempt at a Solution Pauli exclusion...

Homework Statement Hi all. Please take a look at: http://en.wikipedia.org/wiki/Particle_in_a_box My problem is: I do not know how to interpret the eigenfunction of a particle in an infinite square well. We have that the wave function is a function of sine, and Psi_1 has no nodes, Psi_2...

Homework Statement Usually when we solve the problem of the infinite square well we place one wall at the origin and the other one at, say 2L (please notice the 2). We get the eigen-energies E_n = {{n^2 \pi^2 \hbar^2}\over{8ma^2}} and the eigen-functions \psi_n = \sqrt{1\over...

Homework Statement A particle of mass m is in the ground state of the infinite square well. Suddenly the well expands to twice its original size, the right wall moving from a to 2a- leaving the wave function (momentarily) undisturbed. The energy of the particle is now measured. What will be the...

Homework Statement What is the minimum KE of an electron trappen in an infinite square well potential of width a = 0.2nm? Homework Equations The Attempt at a Solution General solution to the simple harmonic oscillator equation: Ψ(x) = Asin(kx)+Bcos(kx) Where the potential of the...

A ptl is initially in its ground state in a box with infinite walls at x=0 and a. The wall of the box at x=a is suddenly moved to 2a. (Energy conserved, wave fn. remains the same, basis changed) We can calculate the probability that the ptl will be found in the ground state of the expanded box...

Homework Statement I am calculating p_{nm} = <\psi_n|p|\psi_m> where \psi_n = \sqrt{2/a}\sin(n\pi x/2). This is for the infinite square well from 0 to a. I think I am messing up: I get that p_{nm} = 0 when n,m are both odd, even and something nonzero otherwise. If I am not messing up I have...

Homework Statement Particle is in a tube with infinitely strong walls at x=-L/2 and x=L/2/ Suppose at t = 0 the electron known not to be in the left half of the tube, but you have no informations about where it might be in the right half---it is equally likely to be anywhere on the right side...

Homework Statement In the early days of nuclear physics before the neutron was discovered , it was thought that the nucleus contained only electrons and protons. If we consider the nucleus to be a one-dimensional infinite well with L=1e-15 m and ignore relativity, compute the ground state...

Homework Statement Infinite square well of length L, from -L/2 to +L/2. Suddenly the box expands (symmetrically) to twice it's size, leaving the wave function undisturbed. Show that the probability of finding the particle in the ground state of the new box is (8/3 \pi )^2. Homework...

Homework Statement The eignefunctions for a infinite square well potential are of the form \psi_n} (x) = \sqrt{\frac{2}{a}} \sin \frac{n\pi x}{a}. Suppose a particle in this potnetial has an initial normalized wavefunction of the form \Psi(x,0)= A\left(\sin \frac{\pi x}{a}\right)^5 What...

Problem: Find the momentum-space wave function \Phi_n(p,t) for the nth stationary state of the infinite square well. Equations: \Psi_n(x,t) = \psi_n(x) \phi_n(t) \psi_n(x) = \sqrt{\frac{2}{a}}\sin(\frac{n\pi}{a}x) \phi_n(t) = e^{-iE_n t/\hbar} \Phi_n(p,t) =...

Homework Statement Consider the infinite square well described by V = 0 if 0<x<a and v = infinity otherwise. At t=0, the particle is definitely in the left half of the well, and described by the wave function, \psi (x,0) = \frac{2}{\sqrt{a}}sin\left \frac{2 \pi x}{a} \right if 0 < x <...

Homework Statement You don't need it verbatim. I'm just trying to solve for the eigenstates and eigenvalues of the Hamiltonian for a one-dimensional infinite square well, with a particle of mass M inside. I'm embarrassed to say it, but the question is throwing me off because the infinite well...

Question: A particle of mass m moves in 1-D infinite square well. at t=0, its wave function is \Psi\left(x,t=0\right)=A\left(a^{2}-x^{2}\right). Find the probability that the particle is in the energy eigenstate E_{n}. Does the probability change with time? What I have so far: So far I...

Consider a particle of mass m in the normal ground sate of an infinite square well potential of width a/2. Its normalized wave function at time t=0 is given by \Psi(x,0) = \frac{2}{\sqrt{a}} \sin \frac{2 \pi x}{a} for 0 <x <a/2 0 elsewhere At this time the well suddenly changes to an...

I think I'm on the right track for this problem, but I'm not entirely sure. Find the solutions to the one-dimensional infinite square well when the potential extends from -a/2 to +a/2 instead of 0 to +a. Is the potential invariant with respect to parity? Are the wave functions? Discuss the...

A particle is in ground state of an infinite square well. Find the probabilirt of finding the particle in the interval \Delta x = 0.002L at x=L. (since delta x is small, do not integrate) here's what I have: \Psi*\Psi = P(x) = \frac{2}{L} sin^2 \left(\frac{ \pi x}{L} \right) \Delta x P...

I need a little help with the strategy on this question. My work is below the problem description. A particle of mass m is in an infinite square well of width a (it goes from x = 0 to x = a). The eigenfunctions of the Hamiltonian are known to be: \psi_{n}(x) = \sqrt{\frac{2}{a}}...

In the infinite square well potential, the obtained wavefunction is, \psi = \sqrt\frac{2}{a} sin \frac{n\pi x}{a} and we know that the Hamiltonian commutes with the momentum operator, which implies that the eigenfunctions for the Hamiltonian is exactly the same for the momentum...

This is a problem from my introductory quantum mechanics class. It's Griffifth's problem 2.6, if anyone has that book. The problem says to investigate the effect of adding two steady state solutions with a relative phase. Namely: \Psi(x,0) = A [ \psi_1(x) + e^{i \phi} \psi_2 (x) ]...