What does the Schrödinger equation mean and how does half-integer spin work?

[Swankie]

Hi all,

In class I've recently been taught the Schrödinger equation and about spin(couple weeks apart). My questions are-

1. In laymans terms, what exactly does the S-eqn mean? What I have taken it to be so far, is an equation that determines the probability of the position of an e- in "orbit" around the nucleus

2. I get the full integer 1,2,3... spin, but what exactly does it physically mean to have 1/2 spin?

I searched a bit for clear answers but have come up with nil so far =)

 

[Fightfish]

The Schrödinger equation is the quantum analogue of Newton's Second Law. It describes the evolution of a wavefunction ψ, where we intepret |ψ|² as the probability density function for the particle.

 

[jfy4]

spin 1/2 is just a number. Its the spin-angular momentum measured in units of $\hbar$. That is, $\hbar /2=5.272859\times 10^{-35}\;\text{joule}\cdot\text{sec}$. If something has spin 1/2 or half-integer spin it means the possible outcomes of measurements of spin for that thing are half-integers of hbar, like, 1/2, 3/2, 5/2, etc...