How Do You Normalize the Wavefunction Ψ(x) in Quantum Mechanics?

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SUMMARY

The normalization of the wavefunction Ψ(x) in quantum mechanics is achieved through the integral <Ψ|Ψ> = ∫|Ψ(x)|^2 dx. The wavefunction is expressed as Ψ(x) = ∫(dk/2π) f(k) uk(x), where f(k) and uk(x) must be defined for proper computation. To normalize the wavefunction, one must compute the integral of the squared modulus of Ψ(x) over the entire space. This process ensures that the total probability of finding a particle in the defined space equals one.

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  • Knowledge of Fourier transforms in quantum mechanics
  • Concept of probability density in quantum mechanics
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Guey

Homework Statement


State from the wavefunction:

Ψ(x) = ∫(dk/2π) f(k) uk(x)

Calculate the normalization <Ψ|Ψ>

Homework Equations


<Ψ|Ψ> = ∫|Ψ(x)|^2 dx

The Attempt at a Solution


[/B]
Well I know the relevant equations, but I am not sure how to compute the integral in order to start normalizing.
Would like a little guidance
 
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Guey said:
Well I know the relevant equations, but I am not sure how to compute the integral in order to start normalizing.
Would like a little guidance
As per PF rules, you have to give some indications of what you have tried.

Also, you should state what ##f(k)## and ##u_k(x)## are.
 

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