Recent content by dudy

is there a more specific rule? take for example: H = a^\dagger e^{-i\omega t} + a e^{i\omega t} (here a is the annihilation operator). This Hamiltonian is of course time-dependent, but, non-the-less, it is also true that: \frac{dA(t)}{dt} = \frac{i}{\hbar} U^\dagger[H,a]U...

Hello, The time-derivative of an operator A(t) = U^\dagger a(t)U in the heizenberg picture is given by: \frac{dA(t)}{dt} = \frac{i}{\hbar} [H,A(t)] + U^\dagger(\frac{da(t)}{dt})U Now, I know that under some conditions, we can write: \frac{dA(t)}{dt} = \frac{i}{\hbar} U^\dagger[H,a(t)]U +...

Hey, We saw in class that rotating a spin state with an angle of 2pi returns minus the state, and so it has to be rotated 4pi rad in order to return to the original state. However, we also saw that the expected value of the spin DOES return to its original value after a rotation of 2pi rad...

Thank you very much for the reply! I still don't understand a couple of things.. a. How could m=0 be the ground state, when its energy is 0, and the energy of the other two hamiltonian eigenstates are negative. shouldn't the ground state have the lowest energy? b. what physical mechanism...

Hello, Given the hamiltonian : H = -( aS_z^2 + b(S_+^2 +S_-^2) ) with S=1 and a,b>0 are constants. working with the base: { |m=1> , |m=-1> , |m=0> } The matrix form of H is: H = \left( \begin{array}{ccc} -ah^2 & -bh^2 & 0 \\ -bh^2 & -ah^2 & 0 \\ 0 & 0 & 0 \end{array}...

Wow. Thank you! Very helpful

Hi, A general question.. In analytical mechanics, we take a given hamiltonian and re-write it in term of generalzed coordinates. In a way- we recode the hamiltonian to concern only the "essence" of the problem. However, it seems to me, that in QM we do the opposite- we look for operators that...

in this formula the ring is centered at the origin, so its the same

that was my guess aswell, but B is proportional to I/r, and so the smaller r is- the greater the ring's contribution to the field.

Hello, Say I have two concentric conducting rings, where r1 >> r2 (why is this important, btw?), and I run a time alternating current I(1) thru the larger one. This will create a magnetic field B (also) thru the smaller ring, which in turn will create itself a magnetic field B2 and so on...

First of all thank you very much for the reply- it is extremely helpful. About the method I'm using- What I did is to take two points from my data that are far apart on the time-line, but have very close values, and watch how the difference (of values) between them grows with time. I repeated...

Hello, Analyzing data from a chaotic pendulum, I calculated the Lyapunov exponent to be somewhere around 10^5 . While my gut tells me something is wrong with this number , i failed to find any information regarding the order of magnitude of Lyapunov exponents and their meaning. Can someone...

I don't understand the following regarding spin: 1. How come you can express the up and down spins in any given direction, using the |+>,|-> in the z direction? 2. Why do I need two vectors (|->,|+>) to express a quantity that can only be either (1) or (-1) ?

got it, thank you!

Let A be an observable (opeator), and we're assuming that for a given state psi(x), the value of A is given by A acting on psi(x), namely - A|psi>. Also we assume that - P(x) = |psi(x)|^2 So, I'de expect the Expectation value of A to be defined like so: <A> = Integral[-Inf:+Inf]{ P(x) A...