Normalizing Psi when it has no complex numbers

In summary, when finding the magnitude of psi for integrals with x between 0 and a, the equation is A^2*(x^2/a^2). However, the complex conjugate can also be used, but in this case it is not necessary since the function is real.
  • #1
DragonPetter
830
1

Homework Statement



I need to square the magnitude of psi for each of my integrals

Homework Equations



for x between 0 and a, [tex]\psi(x,0)[/tex] = A(x/a), where A and a are constants

The Attempt at a Solution


So I take A(x/a) and square it since it is already positive. so [tex]A^2\ast(x^2/a^2)[/tex] . . but in the proof of my book, it makes use of the complex conjugate, which I am sure of how that fits for my particular psi function . . which makes me think that [tex]A^2\ast(x^2/a^2)[/tex] is not correct


so is [tex]|\psi|^2[/tex] = [tex]A^2\ast(x^2/a^2)[/tex] if [tex]\psi[/tex] = A(x/a)
in this example?
 
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  • #2
Yes. The complex conjugate of a real function is the function itself.
 
  • #3
Hmm, so i am worrying over nothing. I am so new to this that I don't really understand why the wave function would have a complex number in it sometimes and other times not have it, since I don't even really know what reason a complex number is for in a wave function.
 

FAQ: Normalizing Psi when it has no complex numbers

What does it mean to normalize psi when it has no complex numbers?

Normalizing psi when it has no complex numbers means reducing the wave function of a quantum system to a real-valued function without any imaginary components. This is often done in quantum mechanics to simplify calculations and make the results more intuitive.

Why is normalizing psi important?

Normalizing psi is important because it ensures that the total probability of finding a particle in all possible states is equal to 1. This is a fundamental principle in quantum mechanics and allows us to make accurate predictions about the behavior of subatomic particles.

How is psi normalized when it has no complex numbers?

When psi has no complex numbers, it is normalized by dividing the wave function by its norm, which is the square root of the integral of the absolute value of the wave function squared. This ensures that the total probability is equal to 1.

Can psi be normalized if it has complex numbers?

Yes, psi can still be normalized if it has complex numbers. In this case, the norm is calculated by taking the square root of the integral of the wave function multiplied by its complex conjugate. This ensures that the total probability is still equal to 1.

What are the benefits of normalizing psi when it has no complex numbers?

Normalizing psi when it has no complex numbers simplifies calculations and allows for a more intuitive interpretation of the wave function. It also ensures that the total probability is equal to 1, which is necessary for accurate predictions in quantum mechanics.

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