I have the opportunity to pursue an independent study in functional analysis (using Kreyszig's book) or calculus on manifolds (using Tu's book) next semester. I think that both of the subjects are interesting and I would like to study them both at some point in my life, but I can only choose one...
It doesn't make too much of a difference as far as my issue is concerned, but for the sake of accuracy, the second expression for the phase should be -\frac{i}{\hbar}\epsilon_r p^{\mu} x_{\mu}. I see that this is in agreement for the positive energy solutions, but my problem still exists for the...
I am working through Greiner's text on relativistic quantum mechanics and I am confused about what appear to be two somewhat contradictory ways of presenting the solutions of the Dirac equation. In chapter 2, he just treats the equation as a system of coupled differential equations and solves...
This is a pretty basic question, but I haven't seen it dealt with in the texts that I have used. In the proof where it is shown that the product of a spinor and its Dirac conjugate is Lorentz invariant, it is assumed that the gamma matrix \gamma^0 is invariant under a Lorentz transformation. I...
By the pointer momentum, I am referring to the observable of the measuring apparatus that is coupled to the observable that is being measured in the system. I don't know if that helped at all, so here is a link that explains the setup...
I am writing a paper on the problem of measurement and I am stuck on what the pointer momentum corresponds to physically. The coupling of the pointer momentum with the observable being measured is used to define the interaction Hamiltonian between the measuring apparatus and the system being...
I am currently in a modern physics course and would to do more advanced study in quantum mechanics before taking the senior-level Quantum Mechanics course at my school. We use Townsend's modern physics book for the class that I am in right now; here is a link...
Definition of "Pointer"
I am in the process of writing a review-type paper for my intermediate quantum mechanics course. I have chosen to do my paper on the topic of measurement, with a focus on weak measurement. In all of the papers that I am reading, the term "pointer" is thrown around, but I...
I would like some clarification as to the mathematical and physical definitions of the position variables in the wave function. I often see that it is treated as a variable independent of time; this is utilized in the separation of variables technique. However, the Schrodinger equation implies...
That realization I had about the partial derivative was the key to solving the problem. Although I haven't figured out how to derive Hamilton's principle from the principle of virtual work, I figured that I'd post the solution in case anyone else happens to encounter my difficulties. The virtual...
I understand that accepting Hamilton's principle will yield identical results as accepting Newton's laws. However, simply accepting that the integral of the difference between kinetic and potential energies is an extrema seems not intuitively obvious. The textbook that I used for my classical...
I was referring to the spatial components of 4-velocity as robphy stated. I am currently working through a textbook and I didn't read the section on the energy-momentum 4-vector before posting this. After reading that section and your responses, it has helped to clarify my interpretation of the...
I understood the derivation of relativistic momentum, but I am uncertain of how to exactly interpret it. One could interpret the arrangement of terms to be relativistic mass times velocity, and this appears to be in agreement with data from particle accelerators (or so I have been led to...
What exactly do you mean by mathematical memory? I haven't gotten into the higher level mathematics courses yet, but I am eager to learn. I'm assuming that this is likely to be something different from a probabilistic memory. I have seen an example where the operator was applied to a...
Thank you for all the responses, you have been very helpful. I have been studying this independently, but I am considering doing a focused inquiry with a professor to speed things along a little more. This would consist of weekly meetings with the professor for an hour working through the theory...