Have a look at this postHaynes 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.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?
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.
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.
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.
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.
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.