@mfb I was taking it as axiomatic that a proton is spherically symmetric. I think it follows that a proton cannot have properties that make some direction special. The drawings in my chemistry book made it looks like these p orbitals designate special directions.
I think the comments...
I'm trying to understand electron orbitals. I'm a beginner. I'm looking at the shapes of p orbitals in a chemistry book, and it's talking about Hydrogen. I'm surprised to see that the orbitals are not spherically symmetric. How can that be when the nucleus is spherically symmetric? Can a...
Thanks for your replies. I'm finding the discussion at https://www.physicsforums.com/showthread.php?t=287383&page=2 very helpful, and it didn't previously turn up in my searches. As I'm beginning to understand, we need a function that represents a probability density and is also wavelike, and...
Regarding the post at https://www.physicsforums.com/showpos...1&postcount=13 , I had read that before posting my question but I was hoping for more--not just that it can be done without reference to the complex numbers, but *why* the complex numbers are appropriate, and why we choose to use them.
I'd like to know why wave functions are taken to be complex-valued in general, and where the i in the Schrödinger equation comes from and what it means. I've seen plenty of we-use-this-because-it-works type arguments. What I'm hoping for is a meaningful explanation of how the complex numbers...