1 - 8 of 8 Chapters
[The Dirac equation is a first order 4×4-system of partial differential equations of the form1]
[The present chapter will be irrelevant1 for the mathematical deployment in succeeding chapters. We offer this material only to provide a motivation for our claim that a Dirac observable should be a self-adjoint pseudodifferential operator.]
[Spectral theory of the Dirac Hamiltonian H of (1.0.2) has been vigorously pursued since the early 1930-s.]
[In this and the following chapter we will investigate time-dependence of ψdoobservables when physical states are kept constant in time. In particular we look for “smooth” dependence on t in uniform operators norms (of our weighted Sobolev spaces). Clearly the exponential operator e-iHt - for...
[In this chapter we will start by discussing a precise theorem giving a necessary and sufficient condition for smoothness of the (inverse) Heisenberg transform, with some “framing conditions” added. Note, the symbol classes ψcm carry a “topology” (in fact, a Frechet topology), defined by the sup...
[It is known and very essential to Dirac’s theory that it is compatible with a transformation of coordinates under the laws of special relativity. In other words, if we change the (space-time) coordinate system by a Lorentz transform then Dirac’s equation remains intact - except for the...
[In this chapter we will analyze the spectral theory of a few of our “precisely predictable approximations” of dynamical observables, which are not precisely predictable. Let us emphasize again: We are not attempting to redefine these observables. The approximations only are good for calculating...
[In this chapter we shall venture beyond the Dirac equation - so far our only object of study - and try reflecting on other wave equations in Quantum Mechanics. Perhaps we have fortified our opinion that - for the hydrogen atom - and, more generally, any “one-particle problem” considering a...
Read and print from thousands of top scholarly journals.
Continue with Facebook
Log in with Microsoft
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Sign Up Log In
To subscribe to email alerts, please log in first, or sign up for a DeepDyve account if you don’t already have one.
To get new article updates from a journal on your personalized homepage, please log in first, or sign up for a DeepDyve account if you don’t already have one.