5
votes
3answers
111 views

Is it true that the Schrödinger equation only applies to spin-1/2 particles?

I recently came across a claim that the Schrödinger equation only describes spin-1/2 particles. Is this true? I realize that the question may be ill-posed as some would consider the general ...
1
vote
2answers
184 views

Representation of Hamiltonian in terms of “creation” and “destruction” operators

Let's have Schrodinger equation or Dirac equation in Schrodinger form: $$ i \partial_{0}\Psi = \hat {H}\Psi . $$ Sometimes we can introduce some operators $\hat {A}, \hat {B}$ (the second is not ...
0
votes
1answer
478 views

Solution to Klein-Gordon equation always valid?

We know that there is a relativistic version of Schrodinger equation called Klein-Gordon equation. However, it has some problems and due to these problems, there is Dirac equation that handles these ...
1
vote
1answer
244 views

Complete set and Klein-Gordon equation

In http://www.physics.ucdavis.edu/~cheng/teaching/230A-s07/rqm2_rev.pdf, it says that when there is some external potential, the Klein-Gordon equation is altered, and it says the following: The ...
2
votes
1answer
383 views

Explanation of equation that shows a failed approach to relativize Schrodinger equation

I'm reading the Wikipedia page for the Dirac equation: $\rho=\phi^*\phi\,$ ...... $J = -\frac{i\hbar}{2m}(\phi^*\nabla\phi - \phi\nabla\phi^*)$ with the conservation of probability ...
2
votes
2answers
723 views

How to obtain Dirac equation from Schrodinger equation and special relativity?

I'm reading the Wikipedia page for the Dirac equation: The Dirac equation is superficially similar to the Schrödinger equation for a free massive particle: A) ...
4
votes
4answers
1k views

Where is spin in the Schroedinger equation of an electron in the hydrogen atom?

In my current quantum mechanics, course, we have derived in full (I believe?) the wave equations for the time-independent stationary states of the hydrogen atom. We are told that the Pauli Exclusion ...