I understand that waves are function of space and time in nature, so E(x,t) will be fundamental description of a wave. I notice that often people denote a wave as E(t) for instance, an envelop function of a pulse. For this case, E is an oscillation at a fixed spatial point x? So that the point x...
I need to learn about Hamiltonian mechanics involving functional and functional derivative...
Also, I need to learn about generalized real and imaginary Hamiltonian...
I only learned the basics of Hamiltonian mechanics during undergrad and now those papers I read show very generalized version...
I am stuck on like the first page of thermal physics. It seems like the signs of the work done on the system are opposite when the volume is expanded and compressed. But when I imagine myself pushing or pulling the piston, I get confused from W = \textbf{F}\cdot \textbf{d}
This work will be...
Boyd - Nonlinear Optics page 5, there says 'Here a laser beam whose electric field strength is represented as $$\widetilde{E}(t) = Ee^{-iwt} + c.c$$But why is it written like this? Is it because the strength is the real part of the complex electric field? Then why doesn't he divide it by 2 after...
Hi, I am a fourth year physics student currently enrolled in a research project course with a supervisor. It's a research in optics and I need to learn about some nonlinear optics.
For the report, I want to write about what I have learned during the term, for instance, Rayleigh and Raman...
Hi,
I am wondering why every general solution to Schrodinger equation can be built from separable solutions. In other words, I don't follow that why every solution to Schrodinger equation can be written as
$$\Psi(x,t) = \sum c_n\Psi_n(x,t)=\sum c_n\psi_n(x)\phi_n(t)$$
I know that the right hand...
The principle of the least action, that the particle will take the path of least Lagrangian, here given as T-U, is Hamilton's principle in classical mechanics. I am wondering if this is just an empirical, experimental observation that is not mathematically driven from elsewhere, just like...
According to one of the postulates of quantum mechanics, every measured observable q is an eigenvalue of a corresponding linear Hermitian operator Q. Which means, that q must satisfy the equation Qψ = qψ. But according to Griffiths chapter 3, this equation can only be followed from σQ = 0. It...
I am following Griffiths' intro to quantum mechanics and struggling(already) on page 16. When a particle is in state ##\Psi##,
$$\frac{d<x>}{dt} = \frac{i\hbar}{2m}\int_{-\infty}^{\infty} x\frac{\partial}{\partial t}\bigg (\Psi^*\frac{\partial \Psi}{\partial x}-\frac{\partial \Psi^*}{\partial...
Homework Statement
For a volume charge, ##\textbf{E}(\textbf{r}) = \frac{1}{4\pi\epsilon_0}\int_{all space}\frac{\hat{\gamma}}{\gamma^2}\rho(r')d\tau'##
and I am trying to get the divergence of it.
Homework Equations
The book says
##\nabla\cdot\textbf{E} = \frac{1}{4\pi\epsilon_0}\int_{all...
Homework Statement
My text book states that for point charges ##q_1, q_2, ... ,## where distance between ##q_i## and ##q_j## is ##r_{ij},## the total potential energy U is the sum ## U = \dfrac{1}{4\pi\epsilon_0} \sum_{i<j} \dfrac{q_iq_j}{r_{ij}} ## and specifically mentions not to count them...
Homework Statement
I am having trouble understanding how a Faraday cage works.
Homework Equations
$$\oint \vec{E}\cdot\,d\vec{A} = \dfrac{Q_{encl}}{\epsilon_{0}}$$
The Attempt at a Solution
It says that Faraday cage is a hollow metallic conductor and hence, inside the cage, $$\vec{E} = 0$$
I...
I'm a 4th year student in a university in Canada, studying pure math. My GPA so far is barely about 3.0/4.0. I was young and totally screwed my undergraduate years. I have planned to go to grad school right after I graduate, but these days I feel so regretful about my GPA that even makes me want...
Hi. I am currently studying pure mathematics in the University of Waterloo, Canada. I am graduating next year and I wish to study pure or applied mathematics in States. I have some questions about my GPA and grad schools in States that I may apply to. If I suppose that I can keep up the grades I...