# Calculating Electron Energy in a One-Dimensional Potential Well

• delrepublica
In summary, the width of a potential well for an electron can be assumed to be about 2 A. The energy of an electron (in Joules and in eV) can be calculated from this information for various values of n. The zero-point energy is equal to infinity.
delrepublica
[SOLVED] Energy in a Potential Well

I so need help with this!

"The width of a one-dimensional potential well of an electron can be assumed to be about 2 A (there's a weird-looking bubble on top of the A). Calculate the energy of an electron (in Joules and in eV) from this information for various values of n. Give the zero-point energy."

Ok, so i know that if it's a one-dimensional potential well, the walls have infinetely high potential barriers. In other words, V0 is equal to infinity.

Hi delrepublica! Welcome to PF!

I've no idea how to do that problem …

but I just thought I'd say hello! …

and tell you that you can impress your friends and professors by producing your own "weird-looking bubble": if you type alt-capital-A, it prints Å.

The $$\AA$$ stands for the Swedish name of the physicist $$\AA$$ngstrom,
which is how this practical atomic length unit is pronounced (if you can pronounce Swedish).
Not all quantum wells are infinite square wells, but if this one is, it should be fully worked out in your textbook.

Last edited:
particle in a box (also known as the infinite potential well or the infinite square well) is a problem consisting a single particle inside of an infinitely deep potential well, from which it cannot escape, and which loses no energy when it collides with the walls of the box. In classical mechanics, the solution to the problem is trivial: The particle moves in a straight line, always at the same speed, until it reflects from a wall.

The problem becomes very interesting when one attempts a quantum-mechanical solution, since many fundamental quantum mechanical concepts need to be introduced in order to find the solution. Nevertheless, it remains a very simple and solvable problem. This article will only be concerned with the quantum mechanical solution.

The problem may be expressed in any number of dimensions, but the simplest problem is one dimensional, while the most useful solution is the particle in the three dimensional box. In one dimension this amounts to the particle existing on a line segment, with the "walls" being the endpoints of the segment.

In physical terms, the particle in a box is defined as a single point particle, enclosed in a box inside of which it experiences no force whatsoever, i.e. it is at zero potential energy. At the walls of the box, the potential rises to infinity, forming an impenetrable wall. Using this description in terms of potentials allows the Schrödinger equation to be used to determine the solution.

Thank you guys so much for your help!
And yes, the A is angstroms, which made everything sooo much easier!

All I needed to do to solve it was use the equation En = [(Dirac's constant)^2 * pi^2 * n^2] / [2m* L^2]

and for the zero-point energy you just use n=1, so easy enough =)

## 1. What is a potential well?

A potential well is a region in which a particle or system of particles experiences a force that pulls it towards a stable equilibrium position. The potential energy of the particle(s) is lower at this equilibrium position compared to points outside of the well, creating a "well" shape in the potential energy graph.

## 2. What is the role of energy in a potential well?

The energy of a particle in a potential well is converted between kinetic and potential energy as the particle moves. As the particle moves towards the equilibrium position, its kinetic energy decreases and potential energy increases. As it moves away from the equilibrium position, the opposite occurs.

## 3. What factors affect the energy of a particle in a potential well?

The energy of a particle in a potential well is affected by the depth and shape of the well, as well as the initial position and velocity of the particle. In addition, the presence of other particles or external forces can also affect the energy of the particle.

## 4. How is the energy of a particle in a potential well related to its stability?

The stability of a particle in a potential well is determined by its energy. If the particle has enough energy, it can escape the potential well and move towards higher energy states. On the other hand, if the particle's energy is below a certain threshold, it will remain in the well and be considered stable.

## 5. Can the energy of a particle in a potential well be negative?

Yes, the energy of a particle in a potential well can be negative if the particle is in a bound state. This means that the particle's kinetic energy is lower than the potential energy at the equilibrium position, resulting in a negative total energy. In contrast, a particle in an unbound state would have a positive total energy.

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