Square well Definition and 223 Threads

Hello, I have a quick question: While working on a problem involving a particle in a harmonic oscillator potential, I had to compute the average kinetic energy at t=0. My question is: would that average kinetic energy be the same or different if the particle was in the same state, but in a...

I am a second year physics student and have been set a homework assignment to solve a one dimensional time independant schrodinger equation in a finite square well using microsoft excel. I understand the physics behind the situation but am not exactly sure how to use microsoft excel to solve...

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) =...

Hi guys, this assignment is driving me nuts! Thank you very much for the help! Homework Statement Consider the infinite square well described by V=0, -a/2<x<a/x, and V=infinity otherwise. At t=0, the system is given by the equation \Psi(x,0) = C_{1} \Psi_{1}(x) + C_{2} \Psi_{2}(x)...

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...

Hey, I'm considering a square well which is finite on one side (left) and infinite on the other (right). So the wave function is: Left-most region: Ae^(ikx) + Be^(-ikx) Inside the well: Csin(lx) + D(cos(lx)) Right-most region: 0 where k and l are known. The problem is with...

Hey, An electron is in a finite square well of 1 Å so the question is to find the values of the well's depth V0 that have exactly two state ? How to proceed with this - finding the eigenvalues En = \hbar^2\pi^2 / 2ma^2 Thanks in advance

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}}...

Hi, I hope this is the right place to ask this... it's problem I have with a homework question but I think it's just me being stupid. There must be something I'm missing. Also I apologise this isn't typed up in proper maths font or anything like I've seen some people doing on this forum... how...

This comes from http://ocw.mit.edu/NR/rdonlyres/Physics/8-04Quantum-Physics-ISpring2003/44AEFEB2-BD59-4647-9B54-3F2C57C2B57C/0/ps7.pdf" of the MIT coursework online. This problem seems straightforward to me and I believe I'm making a stupid math mistake of one kind or another, though its...

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...

I read through the derivation of bound and scattering states for a finite square well. The logic made sense to me, but I am not entirely sure how to accommodate an arbitrary initial wave function (with mean E < 0). Afterall, there are only a finite number of bound states. My guess was that the...

Hi, I have a problem with the finite square well. I have to analyze the odd bound states of the finite square well, V(x)= \begin{cases} -V_0 & \text{for } -a<x<a\\ 0 & \text{otherwise} \end{cases}. Specifically, I have to examine the limiting cases (wide, deep well and narrow...

Is there any website where I can find the analytic form of the eigenenergy of a 1-D finite square well potential?

I'm trying to normalize the even wave functions for the finite square well. The wave function is: \psi(x)= \begin{cases} Fe^{\kappa x} & \text{for } x< a\\ D\cos(lx) & \text{for } -a\leq x \leq a\\ Fe^{-\kappa x} & \text{for } x> a \end{cases} How can I determine D and F? When I...

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) ]...

Edit: I corrected an error in the "normalizing" (forgot to square the functions). But since I wasn't really using it anyway it doesn't seem to matter. This square well has an infinite wall at x=0 and a wall of height U at x=L. For the case E < U, obtain solutions to the Schrodinger...