Normalizing a Wavefunction for the Cyclopentadienyl Radical

In summary, to normalise the wavefunction for the cyclopentadienyl radical using the Huckel approximations, first multiply the wavefunction by a constant, then square it. The result should be N=1/5.
  • #1
baldywaldy
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Homework Statement


Assuming the five basis atomic orbitals are normalised use the Huckel approximations to normalise the wavefunction for the cyclopentadienyl radical
Wavefunction = [tex]\phi_{1}+\phi_{2}+\phi_{3}+\phi_{4}+\phi_{5} [/tex].


Homework Equations



I know that [tex]\phi_{i}\phi_{j}[/tex] = 1 if i=j and 0 otherwise and I know that to normalise a wavefunction you square it and times by a constant.

In the end I got N=1/5
 
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  • #2
baldywaldy said:

Homework Statement


Assuming the five basis atomic orbitals are normalised use the Huckel approximations to normalise the wavefunction for the cyclopentadienyl radical
Wavefunction = [tex]\phi_{1}+\phi_{2}+\phi_{3}+\phi_{4}+\phi_{5} [/tex].


Homework Equations



I know that [tex]\phi_{i}\phi_{j}[/tex] = 1 if i=j and 0 otherwise and I know that to normalise a wavefunction you square it and times by a constant.
You're close, but you have things in wrong order.

First, you multiply the wavefunction by a constant.

Then you square it.

In the end I got N=1/5
Following my suggestion will change that answer.
 

1. What is the purpose of normalizing a wavefunction?

Normalizing a wavefunction means adjusting its amplitude so that the total probability of finding a particle in any location is equal to 1. This is important because probability is a fundamental concept in quantum mechanics and a wavefunction must accurately represent the probability of finding a particle in any given location.

2. How is a wavefunction normalized?

A wavefunction is normalized by calculating its normalization constant, which is the inverse square root of the integral of the wavefunction squared over all space. This constant is then used to adjust the amplitude of the wavefunction so that its total probability is equal to 1.

3. Is it always necessary to normalize a wavefunction?

In most cases, it is necessary to normalize a wavefunction in order to accurately represent the probability of finding a particle in any location. However, there are some situations where a wavefunction may already be normalized, such as in a stationary state of a particle in a one-dimensional box.

4. What happens if a wavefunction is not normalized?

If a wavefunction is not normalized, it means that the total probability of finding a particle in any location is not equal to 1. This can lead to incorrect predictions and interpretations of quantum mechanics, as the wavefunction does not accurately represent the probability of finding a particle.

5. Can a wavefunction be normalized to a value other than 1?

No, a wavefunction must be normalized to a value of 1, as this represents the total probability of finding a particle in any location. Normalizing to any other value would result in an incorrect representation of the probability and would not follow the fundamental principles of quantum mechanics.

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