For example, say you start out with (2,1,0) and (2,0,2). Well the easiest answer here is to think of these two vectors in a plane, so you should take the cross product to get the vector that is not in the plane, and there you have a basis for R^3. But how about when we run into similar problems...
I'm a Mac user and I'm looking for some sort of file where I could refer to a bunch of examples of LaTeX equations from PDE, Matrices, ODE, Analysis, Algebra etc. like
\frac{\hbar}{i} \frac{\partial}{\partial t} \psi (x,t) = H \psi
So I could do more cutting and pasting as opposed to...
This all is very vague, I find a lot of explanation lacking. I am looking for some sort of formulation where we can have an observation operator of some sort, so when we look at it together with the wave function we have the evolution of the wave function by being changed by the observation. It...
I know that in QM, one observation like position will alter the wavefunction so that momentum changes. But how do we see this mathematically when we include time dependence, whether in matrix mechanics or wave mechanics? Is it as simple as writing PQx where x is the state, Q position matrix, P...
Ok, so in other words can we say a magnetic field, being that it is a result of moving charge is composed of three things:
1. the quantum orbital angular momentum L = r x p = B_1
2. the spin magnetic moment written as B_2
3. a component derived from the velocity of the actual electron using a...
Apologies for any vagueness or ignorance here (and lack of citations) but I remember reading that ferromagnetism arises from spin behavior of many electrons. So in a broader sense, are all magnetic fields arising from spin? I am trying to understand how magnetic fields can be viewed at the...
Does that mean stationary states do not obey the Uncertainty Principle in the usual sense? We would need a sort of limiting process that would this work. I am having a hard time understanding this. I imagine a function like a gaussian being the phi(q) and then it multiplied by the phase factor...
What I know: In stationary states the time dependence is factored out so it is of the form phi(q) * e^(-i omega t), thus in its appearance there is no wave function spread. However I recall from texts that wave packet spread is considered a universal phenomena in quantum mechanics, so I am...
I have books (Quantum Theory by Bohm for example) with derivation of the spread of the wavefunction of a free particle in the Schrodinger equation. But does this spreading only happen as a free particle? What about under the general Schrodinger equation where there exist potentials that seem to...
In chemistry I learned the bonding rules that I learned for various molecules never mentioned anything about the different energy levels in electrons. Now that I know electrons can have various energy levels from absorption of photons, I would like to know if this changes the behavior of...
For me physics forums would be a better place if it were more organized according to topic. For example, if someone posts a question about light reflection in quantum physics, that there can be a sort of hierarchy of topics in quantum physics, so it can be tagged and found there. So if someone...
I have searched topics like reflection forum and I always seem to get different answers. I'm hoping to reconcile all of this, I've read FAQs, threads, wikipedia...
To explain reflection I've heard these 3 explanations:
1) Light is absorbed by an atom, then re-emitted at a later time randomly...
so how are the two related then? mathematically the statements of the 2nd law look very different from statistical mechanics to classical thermodynamics, is there a way to "convert" one to the other via relating abstract states of the system to temperature? I'm getting a bit confused because...