When calculating the momentum expectation value

[rwooduk]

when calculating the momentum expectation value the term i(h-bar)d/dx goes inbetween the complex PSI and the 'normal' PSI, so do you differentiate the normal PSI and then multiply by the complex PSI? or do you differentiate the product of the two PSI's i.e. the modulus of PSI?

thanks for any direction on this.

 

[CompuChip]

when calculating the momentum expectation value the term i(h-bar)d/dx goes inbetween the complex PSI and the 'normal' PSI, so do you differentiate the normal PSI and then multiply by the complex PSI?

Yes. The expectation value of $\hat A$ is $\int \Psi^* \hat A \Psi \, dx$ where any differential operators in $\hat A$ works to the right.

 

[vanhees71]

Another hint:
$$\hat{p}=-\mathrm{i} \frac{\mathrm{d}}{\mathrm{d} x}.$$
Note the sign!

 

[rwooduk]

Brilliant! Many Thanks CC!

Another hint:
$$\hat{p}=-\mathrm{i} \frac{\mathrm{d}}{\mathrm{d} x}.$$
Note the sign!

hm, not sure what you're getting at, the negative sign just comes to the front of the integral, I am probably missing something. but thanks also!

 

[vanhees71]

I just wanted to make sure that you get that sign right, because you got it wrong in your original posting!