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Normalization Explained | Physical Significance

Normalization | Quantum Mechanics

What is normalization?

Not only in quantum mechanics but normalization procedure is also used in so many fields.

So, in general, it is a mathematical procedure used to scale values to a common range or standardize them in a particular way.


Why is it necessary to normalize a wavefunction?

It is because it ensures that the total probability of finding the particle in all possible states is equal to 1.

In other words, we can say that,

By normalizing the wave function, we ensure that the probabilities associated with different states of a system are properly defined and consistent.


Normalization Condition

Mathematically, the normalization condition is expressed as the integral of the square magnitude of the wave function over all possible states, which must be equal to 1.

This condition is expressed as:

$\int |\psi(x)|^{2}$ dx = 1

where ψ(x) is the wave function, $|ψ(x)|^{2}$ represents the probability density, and the integral is taken over all possible values of the variable x (which could represent position, momentum, etc.).

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