What is normalised wave function?

A normalised wave function is a wave function that has been adjusted so that its total probability density integrates to one across all possible values. This is a fundamental concept in quantum mechanics, where the square of the absolute value of the wave function at a given point represents the probability density of finding a particle at that location.

Here are the steps to normalise a wave function:

1. Square the wave function: The square of the wave function gives the probability density function. This is because in quantum mechanics, the square of the magnitude of the wave function at a given point gives the probability of finding the particle at that point.

2. Integrate the probability density function: The integral of the probability density function over all space should be equal to one. This is a requirement for a valid probability density function.

3. Adjust the wave function: If the integral of the probability density function is not equal to one, the wave function needs to be adjusted. This is done by dividing the wave function by the square root of the integral of the probability density function. This process is called normalisation.

4. Check the normalised wave function: After normalisation, you should check that the integral of the square of the absolute value of the wave function over all space is indeed equal to one. If it is, then you have a normalised wave function.

In summary, a normalised wave function is a wave function that has been adjusted so that its total probability density integrates to one across all possible values. This is a key requirement in quantum mechanics, ensuring that the total probability of finding a particle somewhere in space is exactly one.