# Why does the square of the amplitude of a wave function represent P?

• I
• Haynes Kwon
In summary, Born's postulate is a fundamental principle in quantum mechanics that states the probability of finding a particle at a certain point is equal to the square of its wave function. While it can be derived to some extent, it is generally accepted as a postulate and cannot be derived in a non-circular manner. This postulate is based on the idea that nature can have discrete outcomes and that probabilities can be represented by a specific operator. However, for those learning quantum mechanics, it is best to accept it as a postulate rather than attempting to derive it from more advanced concepts.
Haynes Kwon
Gold Member
Born's postulate suggests if a particle is described a wave function ψ(r,t) the probability of finding the particle at a certain point is ψ*ψ. How does this work and why?

It’s simply a postulate of quantum mechanics, you can motivate it based on various arguments but it cannot really be derived from anything in a non-circular manner.

Demystifier
Haynes Kwon said:
Born's postulate suggests if a particle is described a wave function ψ(r,t) the probability of finding the particle at a certain point is ψ*ψ. How does this work and why?
It can be derived to a certain degree, but the most general such derivations are quite advanced. If you're still learning QM it is best to accept it as a postulate.

A derivation of it is basically if you acknowledge nature can have discrete outcomes in certain experiments with those outcomes having a certain algebraic relation to each other you can derive that all probabilities must come from a specific operator ##\rho## with the wavefunction being a sort of special case (pure state). See the thread @Mentz114 mentioned as well.

Haynes Kwon

## 1. Why is the square of the amplitude of a wave function used to represent probability?

The square of the amplitude of a wave function is used to represent probability because it is directly related to the likelihood of finding a particle at a certain position. This is known as the Born Rule, which states that the probability of finding a particle at a certain position is proportional to the square of the amplitude of its wave function at that position.

## 2. How does the square of the amplitude of a wave function relate to the wave nature of particles?

The square of the amplitude of a wave function is a measure of the intensity or magnitude of the wave. In quantum mechanics, particles are described as waves, and the square of the amplitude of the wave function represents the probability of finding the particle at a specific position. This shows the wave-like behavior of particles in quantum mechanics.

## 3. Can the square of the amplitude of a wave function be negative?

No, the square of the amplitude of a wave function cannot be negative. This is because probability can only take on positive values, and the square of a negative number is always positive. Therefore, the square of the amplitude of a wave function must also be positive.

## 4. What happens to the probability when the square of the amplitude of a wave function is increased?

As the square of the amplitude of a wave function increases, the probability of finding a particle at a specific position also increases. This is because the amplitude of the wave function represents the intensity of the wave, and a higher intensity means a higher probability of finding the particle at that position.

## 5. How does the square of the amplitude of a wave function change over time?

In quantum mechanics, the square of the amplitude of a wave function can change over time due to the wave function's evolution. This is described by the Schrödinger equation, which shows how the wave function changes over time. As the wave function changes, the square of its amplitude also changes, leading to changes in the probability of finding a particle at a specific position.

Replies
1
Views
1K
Replies
9
Views
844
Replies
1
Views
972
Replies
6
Views
1K
Replies
64
Views
4K
Replies
11
Views
2K
Replies
14
Views
3K
Replies
25
Views
2K
Replies
3
Views
1K
Replies
1
Views
1K