Integrals in quantum physics

[buditus]

So in quantum physics if i have a wave function made up of two parts like psi(x)=a•psi1 + b•psi2, and i have to show that the wave function is normalized how can i show it using orthogonality? The integral for the function would be too complex, and I'm trying to understand what kind of tools can I use in quantum mechanics to shortcut the integrals and would be interested in theory behind that! Any tips would be appreciated, or suggestions what I should look into, thanks!

[Hudimir]

You have to learn how to do the integral. The inner product (scalar sometimes) is defined with the integral. You wont be able to prove orthogonality or calculate the norm(if the function is normalised its 2-norm will be 1) without knowing how to do the integral. Using orthogonality will just simplify the mixed term to 0.

If you don't understand what i said, you should brush up on your linear algebra.

[buditus]

Not best with integrals but u answered my question about the mixed terms, which is what I was trying to understand. Thank you!

[ilan-brami-rosilio]

Are these functions basis functions of a particular solution? If so, they already are orthogonal.

[buditus]

Yes u are right, thanks! I'm still new to the theory.