Hello!(adsbygoogle = window.adsbygoogle || []).push({});

I study mathematics and am in my sixth year, but...

I have a very elementary question:

I stumbled upon it while learning for quantum mechanics. But it's nothing new, it's happening to me all the time: I get confused by things like this!

Observe the following facts:

Suppose we deal with the space of wave functions over the real line.

The wave function [tex]\psi(x)[/tex] is a complex scalar. Take for example [tex]\psi(x)=e^{ikx}[/tex] (not normalizable, don't need it)

The derivative [tex]\psi'(x)=ike^{ikx}[/tex] has 1/length as it's unit.

Integrating that over some interval yields a scalar. [tex]\psi(b)-\psi(a)[/tex]

The probability density [tex]\psi*(x)\psi(x)[/tex] is a scalar.

Integrating this over the real line (length) gives 1. A scalar...

Shouldn't such an operation yield a length? Am I stupid?

I am not joking. For me this is a mystery.

Thanks for your answers.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Very stupid question

**Physics Forums | Science Articles, Homework Help, Discussion**