What is Square well: Definition and 223 Discussions
In quantum mechanics, the particle in a box model (also known as the infinite potential well or the infinite square well) describes a particle free to move in a small space surrounded by impenetrable barriers. The model is mainly used as a hypothetical example to illustrate the differences between classical and quantum systems. In classical systems, for example, a particle trapped inside a large box can move at any speed within the box and it is no more likely to be found at one position than another. However, when the well becomes very narrow (on the scale of a few nanometers), quantum effects become important. The particle may only occupy certain positive energy levels. Likewise, it can never have zero energy, meaning that the particle can never "sit still". Additionally, it is more likely to be found at certain positions than at others, depending on its energy level. The particle may never be detected at certain positions, known as spatial nodes.
The particle in a box model is one of the very few problems in quantum mechanics which can be solved analytically, without approximations. Due to its simplicity, the model allows insight into quantum effects without the need for complicated mathematics. It serves as a simple illustration of how energy quantizations (energy levels), which are found in more complicated quantum systems such as atoms and molecules, come about. It is one of the first quantum mechanics problems taught in undergraduate physics courses, and it is commonly used as an approximation for more complicated quantum systems.
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...
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...