Probability density and wavefunction for harmonic oscillator

[hellomister]

Homework Statement

Does a wavefunction have to be normalized before you can calculate the probability density?

Homework Equations

n/a

The Attempt at a Solution

Im thinking yes? so that your probability will be in between 0 and 1?

 

[Dick]

Homework Statement

Does a wavefunction have to be normalized before you can calculate the probability density?

Homework Equations

n/a

The Attempt at a Solution

Im thinking yes? so that your probability will be in between 0 and 1?

Yes. You normalize it first. But that doesn't mean the probability density is between 0 and 1. If you have x has is definitely between 0 and 1/2 not elsewhere with uniform probability, that's a probability density of 2 between 0 and 1/2. It does mean the integrated probability density will be 1.