Question

WHY IS THE WAVE FUNCTION NORMALIZED

Answer 1

Answer:

Explanation:

Since wavefunctions can in general be complex functions, the physical significance cannot be found from the function itself because the  

√

−1

is not a property of the physical world. Rather, the physical significance is found in the product of the wavefunction and its complex conjugate, i.e. the absolute square of the wavefunction, which also is called the square of the modulus.

Ψ∗(r,t)ψ(r,t)=|Ψ(r,t)|2  

where r is a vector (x, y, z) specifying a point in three-dimensional space. The square is used, rather than the modulus itself, just like the intensity of a light wave depends on the square of the electric field. Remember that the Born interpretation is that Ψ∗(ri)Ψ(ri)dτ is the probability that the electron is in the volume dτ located at ri. The Born interpretation therefore calls the wavefunction the probability amplitude, the absolute square of the wavefunction is called the probability density, and the probability density times a volume element in three-dimensional space (dτ) is the probabilit