I Normalization of wave functions

[Nana113]

TL;DR Summary

Is there any properties of normalisation that can be used when encountering superstition of wavefunctions

If wave functions are individually normalized does it mean that they are also normalized if phi 1 and phi 2 are integrated over infinity?

 

[PeroK]

Can you explain your question more clearly?

 

[vanhees71]

The question in the OP cannot be answered, except one has more information on the three wave functions. E.g., if they are orthonormal to each other, then there's a unique answer.

Also the norm in Hilbert space is of course the norm induced by its scalar product. I.e., in position representation, where the Hilbert space is the space of square-integrable functions, this scalar product is defined as
$$\langle \psi_1 | \psi_2 \rangle=\int_{\mathbb{R}} \mathrm{d} x \psi_1^*(x) \psi_2(x),$$
and thus the norm of a wave function is
$$\|\psi \|=\sqrt{\langle \psi|\psi \rangle}, \quad \langle \psi|\psi \rangle=\int_{\mathbb{R}} \mathrm{d} x |\psi(x)|^2.$$

 

[PeterDonis]

View attachment 338171

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