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Comments:
<0> evening everyone! freakman!
<0> :)
<0> any nonlinear dynamical systems experts around..?
<1> hey jmpp :)
<0> I'm looking for some info on non-autonomous systems
<0> but can't find much
<0> specifically...
<1> too bad I don't that much about physics yet
<0> I'm interested in analysing the equilibria of a non-autonomous system through the eigenvalues of its jacobi matrix
<2> jacobian?
<2> is jacobi different?
<0> jacobian, right
<0> almost everybody does it through floquet theory, which I'm not acquiated with
<0> so I approached the problem with the evaluation of th jacobian at the different equilibria and finding the eigenvalues in each case
<0> but that's a problem if the system is non autonomous
<0> the eigenvalue will depend on the time variable
<2> sounds difficult, not something I'll be able to advise you on
<0> nonlinear dynamics :)
<0> what are you studying at the moment
<0> ?
<2> BS in physics
<0> bs...?
<0> bachelor degree? undergrad?
<2> yeah
<0> yeah, me too :)
<0> but from what I've seen, nonlinear dynamics is not a main stream course, this is an optional one
<2> most nonlinear systems are not done much as undergrads
<3> bonne nuit messieurs / good night gentleman !
<4> I have my mcu all hooked up and working now
<4> with a few simple commands i can turn diodes on and off....
<4> the POWER!
<5> ?
<4> irbdavid: its a microprocessor
<4> it does things...
<0> so, anyone want to give me some advice on non autonomous nonlinear systems, other than using floquet theory? :)
<4> jmpp: i have diodes
<6> i read that as dildoes
<6> im going mad
<4> hehe
<7> sacarasc, just stress
<7> can be bad too though
<8> Hello
<7> hi Ninina
<7> off to bed though
<9> can anyone help me understand quantum probability?
<10> sure, thats a topic easily explain over irc ...
<9> haha, well, do you know of a resource that's pretty good at explaining it?
<11> Quantum probability is easy to explain. You can even test it in a high school physics cl***. The double slit experiment is an excellent example.
<9> synx: i understand the glossed-over stuff (wave-particle duality and such), what i'm trying to understand is the formal mathematical basis for, say, the definition of a random variable in quantum probability.
<11> naura: I don't even know a resource that's bad at explaining that!
<12> explaining what?
<11> Only some small pieces of that I know, such as how the shape of an electron cloud is based on good old angular momentum.
<2> in quantum mechanics...
<2> the analogue for finding the 'equations of motion' in cl***ical mechanics, is to find the 'Wave Function'
<9> Manyfold: quantum probability
<2> A small particle, according to Quantum Mechanics (QM), can be observed at a position, and can be observed to have a velocity
<12> the probabillity is the wave function squared
<2> According to the Heisenberg Uncertainty Principle, you can only know the position very well, or the velocity very well, but not both
<12> depends on your error of measurement
<11> microacg: There is math out there that doesn't ***ume that, and derives it. That's what I can't help with.
<2> Manyfold: what I just said is an absolute truth in QM I believe
<2> QM starts with the Schrodinger Equation
<2> it was not derived
<12> yeah i said nothing against it
<2> the equation was figured out by a clever/lucky guy
<2> it turns out, that equation is verifiable
<2> the wave function is found by solving the Schrodinger Equation
<11> Right, but the schoedinger equation leads you to conclude that you can't know the velocity and the position at the same time, right?
<12> H psi =E psi
<9> well, schrodinger was in the right place at the right time. but what i'm asking is at a simpler level than that, i think
<11> Not the other way around?
<2> I don't think it's either way around
<2> naura, what do you want exactly?
<11> There really is no simpler level than that.
<11> Not that I know at least.
<2> if you want to start with the fundamentals
<2> start with blackbody radiation
<12> synx it's rather easy when you know how a fouriertransform works
<9> we have the cl***ical definition of a random variable - a variable that may take a number of states with a certain probability of each one. what is the analogue in quantum mechanics? how is a random variable defined?
<2> that number is not discretized, I guess
<2> it is continuous
<12> naura: do you know linear algebra?
<11> Manyfold: That's like saying lifting 200 kg is easy when you have lots of muscles. x)
<2> you say that like a fourier transform is ridiculously difficult lol]
<9> Manyfold: i've studied it myself, so i enough some (vector spaces, orthonormal bases, eigenvalues, etc)
<12> synx: i am working on that muscle thing ^
<2> anyway when you solve the schrodinger equation, you get a set of possible solutions by solving an eigenvalue problem (***uming time independent potential)
<2> The eigenvalue of the hamiltonian is a possibly observed energy, and the corresponding eigenstate is the wave function
<12> naura: when you make a measurement in qm you apply an operator(hermitian matrix) to a state
<2> you can see from this this that energy is quantized
<2> learn about: planck's constant
<9> Manyfold: and how exactly is a state represented? a set of vectors in a complex hilbert space?
<2> vectors -> functions
<2> in hilbert space
<2> if I'm understanding the language correctly
<12> looks like this H|psi> where |psi> is an element from some fancy complex vector space
<12> naura: well you surely know that wavemechanical thing H psi
<2> H |psi> = E |psi> yay
<2> (Time independent only)
<12> psi is <r|psi>
<9> with all that bra-ket notation stuff? yeah.
<12> where r is a position eigenstate
<12> nnaura so where are we atm?
<2> it would probably be helpful to demonstrate solving the S.Equation for a simple potential :3
<12> it was something about the measurement process i believe
<12> naura: okay lets take H=p^2/2m + V
<2> 1D?
<12> do you know this?
<12> of course it should be simple
<9> well, i think i get this much: the eigenvectors of H (called |v>) are an orthonormal basis of the Hilbert space, and the eigenvalues E that satisfy H|v> = E|v> are the possible energy levels.
<9> is that correct?
<12> that's right
<12> it's because our opetrator is hermitian
<9> all i know about hermitian operators is taht their matrices are their own conjugate transposes
<12> but back to our H=p^2/2m + V
<9> right, back to that
<2> is p operatore = -i hbar d/dx I forget
<12> now we plugin in the momentum operator for p
<12> so we get with hbar =1
<2> oh changing units are we
<2> gotta be all fancy
<12> d^2/dx^2 /2m + V
<12> i hate writting out hbar every time
<2> is there a minus
<2> no guess not
<2> oh wait
<12> now we plug this into the S.E.
<2> (-i)^2
<2> right?
<12> % -I^2
<2> it's -1
<9> % (-i)^2
<13> naura: i^2
<2> i^2=-1
<9> indeed
<2> thus my original suggestion seems to be correct
<12> % 1+1
<13> Manyfold: 2
<12> % -I^2
<13> Manyfold: 1
<12> whats that?
<2> are you trying to tell me that (-i)^2 is 1?
<2> you need to use paranthesis
<2> ses*
<9> (-i)^2 = i^2 = -1
<12> yeah i have seen that
<2> yes I've been saying that for five minutes
<2> what potential will you use
<2> square well?
<12> - d^2/dx^2 /2m + V
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