Quantum Particles in an Infinite Square Potential Well

quantum number

1

2

3

4

5

6

7

8

9

10

lower limit

0

upper limit

1

This Demonstration shows the probability of finding an electron in an infinite square potential well (top graphic) and also shows the wave function of the electron (bottom graphic).

Details

quantum number — an integer value, one of the discrete quantum states of the electron

lower and upper limits — the lowest and highest x values for the position of the electron

The one-dimensional solution to Schrödinger's equation for an electron in an infinite square potential well (normalized to be of width 1) is

2

sin(nπx)

, where

n

is the quantum number. The square of this wave function is the probability density function for the electron.

The probability of finding the electron somewhere inside the square well is 1. (snapshot 1)

The probability of finding the electron with a quantum number of 3 between 0.2 and 0.8 is approximately 0.54. (snapshot 2)

The probability of finding the electron with a quantum number of 4 between 0.25 and 0.75 is approximately 0.5. (snapshot 3)

External Links

Infinite Square Potential Well (ScienceWorld)

Schrödinger Equation (ScienceWorld)

Permanent Citation

Jeff Bryant

"Quantum Particles in an Infinite Square Potential Well"
http://demonstrations.wolfram.com/QuantumParticlesInAnInfiniteSquarePotentialWell/
Wolfram Demonstrations Project
Published: April 27, 2007