Square well Definition and 223 Threads

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 \\...

hey physicists; I have a question concerning the problem of finding the bound states of a spherically symmetric square well. The solutions of the radial equation inside and outside the well are given by: R(r)=Aj_l(sqrt(2m(V-|E|))*r); R(r)=Bh_l(sqrt(2m|E|)*i*r) respectively, where j_l and...

Homework Statement Comparing the hydrogen atom orbitals to an infinite square well. a.) For the hydrogen atom, what is the energy difference between the ground state and the next energy level? b.) Now 'tune' an infinite square well holding a single electron so that it has the same energy...

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...

Hi I'm a little confused when it comes to measuring the momentum in a infinite or finite square well. Is this even possible? One of the postulates of quantum mechanics states that measuring an observable will leave it as an eigenstate of that observables corresponding operator just after...

I realize there are several practical problems with what I say below, but my question is if anything is _theoretically_ wrong with this. I'm just thinking of the problem in 1 dimension right now and ignoring the interaction potential between the particles and people involved (I don't think...

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...

Consider double finite square well with -Vo; -(a+b/2) < x < -b/2 V(x) = 0; -b/2 < x < b/2 -Vo; b/2 < x < a + b/2 0; otherwise Sketch the ground wave function Psi(n=1) and the first excited state Psi(n=2) for 1. b = 0 2. b~a 3. b >> a So...

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...

I am trying to prove that there is always one bound state for a finite square well using variational method, and I am stuck. I've tried using e^(-bx^2) as my trial wave function, but I am left with E(b)=(hbar^2)b/2m - V, where V is the depth of the well. In this equation, taking the derivative...

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 Just need some rough guidance on this one, nothing specific is really needed. The problem: Given a spherically symmetric potential (V(r)) V\left( r \right) = \left\{\begin{gathered} V_0 \hfill \hspace{2}r<a \\ 0 \qquad a<r<b \\ \infty \hfill r>b \\ \end{gathered}...

Homework Statement Compute \tau for and electron in the double square well potential of width L = 2 Bohr, and depth \bar{V} = 4 and separation R = 3. Use atomic units for your computation. Homework Equations In his lecture notes... he gave us \tau = h/\DeltaE . I don't know where that...

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...

Homework Statement Hi I am trying to apply degenerate perturbation theory to a three dimensional square well v= 0 for x, y,z interval 0 to a, perturbed by H' = xyz (product) from 0 to a, otherwise infinite. I need to find the correction to energy of the first excited state which I know is...

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 Determine the transmission coefficient for a rectangular barrier. Treat seperately the three cases E<Vo, E>Vo, and E=Vo.Homework Equations V(x)= +Vo if -a<xa V(x)= 0 otherwise Transmission coefficient=(amplitude of transmited wave)2/(amplitude of incoming wave)2 I am also...

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 "A particle of mass m is in the ground state of a one-dimensional infinite square well with walls at x=0 and x=a. \psi_1(x) =\sqrt{\frac{2}{a}}sin(\frac{\pi x}{a}), E1=\frac{h^2\pi ^2}{2ma^2}* What is the initial wave function \Psi(x,0)? *h is supposed to be h bar, I...

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...

Homework Statement I have to show that the delta function bound state energies can be derived from the finite square well potential. Homework Equations The wave functions in the three regions for the finite square well. (See wikipedia) The Attempt at a Solution 1. I start from the...

Homework Statement Based on the finite potential well defined by the following equations, how many bound states are there, which of these states are even and which are odd, and what are their energies? V(x)= 0 for x\leq-l/2 and x \geq +l/2 V(x)=-\hbar^{2}/ma^{2} Homework...

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 Find the solutions of even and odd parity from the transcendental equations then find the number of bound states that are possible for a potential such that p(max) = 4? Homework Equations p=ka/2 & p(max)^2 = (u(not)a^{2}/4), u(not) =...

Possible bound states of a one-dimensional square well... I'm Lost! Homework Statement Find the solutions of even and odd parity from the transcendental equations then find the number of bound states that are possible for a potential such that p(max) = 4? Homework Equations p=ka/2 &...

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 Hi all. When talking about the finite square well with a potential V > 0 for - A < x < A, I have never seen an example of bound states (i.e. E<0). They only treat examles with scattering states (i.e. E>0). Is there any reason for this? My book (Griffith's Intro. to QM)...

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...

In the problem of a finite potential well, we search for bound states, in which E<V. Say the potential is defined to be 0 outside of the well, and -V0 inside it. Analyzing the case when -V0 < E < 0, one finds that the probability of finding the particle outside the well is not zero. This...

Homework Statement Consider the SHO inside a square well, which looks like a soda can cut in half inside of a box. \[ V(x,y) = \left\{ \begin{array}{l} \frac{1}{2}kx^2 ,{\rm{ }}y{\rm{ }} < {\rm{ }}|a| \\ \infty ,{\rm{ }}y{\rm{ }} \ge {\rm{ }}|a|{\rm{ }} \\ \end{array} \right\} \]...

Homework Statement consider V(x,y) = inf, |y| > a; 1/2kx^2, |y|<=a. find the energies of this potential. my initial idea was to just look for solutions of the form X(x)*Y(y), and solve for the separation constant, which should give me the energy, right?

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...

If one wall is at infinite potential, and the other at some finite potential, what is the decay length outside of the well? I was thinking it might be twice that for a finite square well. Also can anyone provide some information regarding these wells? Google is (surprisingly) devoid of any...

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...

Hi, My Quantum textbook loves to skip the algebra in its derivations. It claims that the solution for 'T', the transmission coefficient of the wave function (E>0, ie. unbound) is T = \frac{2qke^{-2ika}}{2qkcos(2qa)-i(k^{2}+q^{2})sin(2qa)} Its prior step is to offer two equations (which match...