You might be interested in Section 4.2 of "Introduction to Quantum Mechanics: A Time Dependent Approach" by David J. Tannor on Bohmian mechanics and the classical limit. If you use Squeezed's suggestion and substitute
\psi= A(\textbf{r},t) e^{\frac{i}{\hbar}S(\textbf{r},t)}
then the...
Are you aware of the book "Mathematical Theory of Feynman Path Integrals: An Introduction" by Sergio A. Albeverio, et. al. ? Perhaps that would be of use to you.
I have to interject here that this is where physicists and mathematicians diverge. Remember it was Hilbert who said "Every school boy in Gottingen knows more about four dimensional geometry than Einstein, yet it was he who created General Relativity not the mathematicians."
The history of...
I realize this thread is a bit old, but I would like to draw your attention to something related to quaternions and that is Geometric Algebra. You might be interested in the book Geometric Algebra by Chris Doran and Anthony Lasenby. Geometric algebra actually is one of the Cliffird algebras and...
You might find chapter 16, sections 19 through 24 (pages 378-383) of Bohm's Quantum Theory interesting. He doesn't do what you ask, but he shows some connections between Schrodinger's equation, the Hamiltonian formulation mechanics and Heisenberg's representation of quantum mechanics that may...
You are right that one must be careful in specifying what \delta is, particularly in the context of Nother's theorem where \delta L is often used to denote the variational derivtaive of the Lagrangian. For what it's worth, on pages 89 and 90 of Anderson's Principles of Relativity Physics ...
I have come to this thread rather late so I may have missed references to recent literature, if so I apologize for the duplication. There is a short review article Sudden Death of Entanglement by Ting Yu and J. H. Eberly in the 30 January 2009 issue of Science . Note: the article starts on...
You're welcome. However, I had a few free minutes on my hands and you question interested me so I did a little reading. This is a case where the history of physics can be helpful in sorting things out. Lande introduced his g-factor when attempting to account for the Zeeman effect and according...
I must apologize. When I wrote my previous post it slipped my mind that there is a beautiful little book by Sin-Itiro Tomonga (as you recall ,winner of the Nobel Prize for QED along with Feynman and Schwinger) called The Story of Spin , published by U of Chicago Press. The first chapter is a...
There is a very nice discussion of a naive model of electron spin, and the gyromagnetic ratio in Peebles Quantum Mechanics , pages 198-201. The g-factor was introduced by Goudsmit and Uhlenbeck to account for the behavior of an electron in a magnetic field because naive models of the electron...
No, this formulation of the Dirac equation does not replace one equation with two real ones. The thing that is different about Geometric Algebra is that there are geometric objects that square to minus 1 for each space ( R^n )you are working in. I personally do not know about any application...
Because Geometric Algebra and Quaternions are Clifford Algebras, they have a lot in common. However, there are some subtle differences. See page 34 of the book by Doran and Lasenby for the details. Briefly, Hamilton attempted to identify pure quaternions (no scalar part) with vectors. Doran and...
When I wrote the above, I was under time pressure and what I wrote is misleading at best. What I should have written was: Briefly, very very briefly, it unites the scalar product and a cross product-like operation called the wedge product into one operation called the geometric product...
A real wave equation with real solutions does not have to be second order. The first chapter of G.B. Whitham's book Linear and Nonlinear Waves is devoted to first order wave equations that give rise to shock waves.
Some of you may be interested in Geometric Algebra for Physicists by Doran...
Bohm's Quantum Theory does not discuss Bohmian mechanics. The standard text on Bohmian mechanics is Holland's The Quantum Theory of Motion . The book by Wyatt I mentioned in my previous post is a nice introduction and section 4.2 of Tonnor's Introduction to Quantum Mechanics, A Time...
I am having trouble wrapping my head around statements that seem to imply that complete physical understanding is only to be found in the mathematics used. To illustrate my difficulty let me pose the following examples:
(1) The heat equation (or, if you prefer, the diffusion equation). The...
Perhaps what you want to do is to give your student a way to visualize what an electron is doing when it exhibits the property of spin. (I know the founding fathers of quantum mechanics, particularly Heisenberg were against visualization, but sometimes it helps.) It might be useful to think of...