# Wave Function Terminology - Are these synonyms?

1. Apr 4, 2014

### shanepitts

Are the quantum mechanical terms "probability amplitude" and "probability density" used interchangeably?

2. Apr 4, 2014

### craigi

No.

The probability amplitude is complex.
The probability density is real.

Take the modulus of the probability amplitude and square it to get the probability density.

3. Apr 4, 2014

### shanepitts

Thanks.

So is it safe to say that a complex wave function is a probability amplitude and that its modulus squared is a probability density?

4. Apr 4, 2014

### Staff: Mentor

Safe enough for all practical purposes, provided that the complex wave function in question is a solution to Schrodinger's equation.

5. Apr 4, 2014

### Staff: Mentor

Yes. $\Psi$ is a probability amplitude and $\Psi^*\Psi$ is the corresponding probability density, assuming that $\Psi$ has been normalized so that
$$\int^{+\infty}_{-\infty}{\Psi^*\Psi dx} = 1$$