What is Infinite potential well: Definition and 63 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.
Homework Statement
Consider a particle in a potential ;
V(x)=0\ for\ 0<=x<=L and
V(x)=\infty\ otherwise
. Its wave function is a linear superposition of the lowest two stationary states and given by
\psi(x,t)=\frac{1}{2}*(\sqrt{3}...
Homework Statement
A particle is trapped in an infinite potential well, with the infinite walls at ±a. At time t=0, the wavefunction of the particle is
\psi = \frac{1}{\sqrt{2a}}
between -a and a, and 0 otherwise.
Find the probability that the Energy of the particle is \frac{9...
Homework Statement
An infinite potential well with a box in the middle V = 100, the walls of the box go from -L/2 to L/2.
Homework Equations
Schrodinger's equation.
The Attempt at a Solution
Please help.
Homework Statement
An electron is in a Infinite potential well (1-dimensional box with infinite wall boundary conditions) at the second energy level. The width of the box is L. What is the electron density n(x) as a function of the position x?
Homework Equations
time-independent Schrödinger...
I've got this question and I'm absolutely clueless, any help will be greatly appreciated:
The nth energy level for a particle of mass m confined in an infinite potential well is :
E = h^2n^2/8ml^2
where L is the width of the well and h is Planck’s constant. Assuming that the uncertainty...
hi,
I am not getting idea to solve below problem
A particle of mass m is in a one-dimensional ,rectangular potential well for which V(x)=0 for 0<x< L and V(x)=infinite elsewhere. The particle is intially prepared in the ground state ψ1 with eigen energy E1. Then , at time t=0, the potential...
I've been told about the infinite potential well using quantum-mechanics, with mathematical proof. Is there any websites I can look at to understand this theory with less math, but instead, with a theoratical approach? Would classical-physics be able to describe this result?
thanks
Homework Statement
Hi,
Particle of mass m is found in one-dimensional infinite potential well with walls 0<=x<=a.
In t=0 the normalized wave function is:
\psi(x,t=0)=A[1+Cos(\frac{\pi x}{a})]Sin(\frac{2 \pi x}{a})
find psi(x,t)
Homework Equations
?
The Attempt at a Solution...
Hi I am just found this forum and I was wondering if anyone could help me find out what exactly is a Infinite Potential Well. I am just trying to understand what exactly a Infinite Potential Well is as well as what all the equations are really solving for. Sorry if this has been posted before I...
Hi guys, I am solving the 1D infinite potential well for a particle, but in this case instead of the potential being 0 from -a to a, its shifted to 0 to 2a. I have calculated that the even parity solution is zero.
My question is, I have calculated that k=n*Pi/(2*a) by applying the boundary...
Hi all,
I have an exam tomorrow and this problem concerns me greatly.
An electron is located in an infinitely deep one-dimensional square potential well. The width of the well is 1.00 nm.
(e) Light is shone on the electron causing it to jump from the ground state to the n = 3 state...
Sorry for all the questions - I tend to save them till I'm done with assignments:
Here's the question:
Consider a particle of mass 'm' in a one-dimensional infinite potential well of width 'a'
V (x) = \left\{\begin{array}{c} 0 \ \ \ if \ \ \ 0 \leq x \leq a \\ \infty \ \ \ otherwise...
At t=0 an electron in an infinite potential well has a wave function corresponding to the lowest level of energy. The wave function is equal to the eigenfunction of the Hamiltonian where n=1.
I am asked to calculate the uncertainty of the electron's momentum. I don't really know where to...