[nimbus]

Hey guys, I just started pchem and I'm absolutely loving the concepts. However, our professor makes a bunch of assumptions about our mathematical knowledge. We don't need to take vector or differential to take this pchem course (it is a brief version, but still quite dense), yet we still had to learn partial derivatives and vector workings on the fly.

I have a few things I don't really understand:

1) Psi represents the wavefunction so psi* must represent the complex conjugate? If the wavefunction has no imaginary parts then psi*psi is just psi^2, correct? If the wavefunction has imaginary parts, then can I use i^2=-1 to do away with the imaginary parts?

2) Normalizing for A involves integrating psi*psi along the boundaries predetermined by the problem, usually 0 to a. Do I have to solve for A before I can attempt psi*psi extractions for KE or P (momentum)?

3) Definition of an eigenvalue: If I operate on a function and get that function back plus an omega (some constant in front of the function) then I have an eigenfunction and a discrete eigenvalue? He scolded us on our first quiz because we did not know there was a specific order of operations for operators, meaning xdx(x^3) is not dx(x4) but in fact 3x^3. We all got an eigenvalue of 4 instead of 3 because we had no idea there was an order of operations. If I have complex operators, how do I ensure that I am doing them in the correct order?

Thanks so much!

[tamim83]

1.) Yes, if the wavefunction does not have complex parts, then psi*psi is just psi^2.  Otherwise, to get psi*, you replace all "i" with "-i".  Also, usually when you are looking at observables like the kinetic energy, there will be a "psi*psi" when you find expectation values for them.  This usually gives you an i^2 and rids you of the complex number.  Which makes sense physically, you don't want an "imaginary kinetic energy" .  

2.) Be careful, the 0 to a boundary sound like particle in a box.  These are subject to change when the problem changes.  But yes, you always will want to work with a normalized function, so if its not already, you will need to normalize the wavefunction before doing anything else.  

3.) Yeah, that's a really common mistake so don't feel bad, hopefully your professor wasn't too hard on you.  If you get a complex operator like x(d/dx), you want to do the operation that is immediately to the left of the function first.  So for x(d/dx)x^4, you would take the derivative first and then multiply by x.  

Hope this helps some.