Quantum question: if I'm given the Hamiltonian H and initial state |phi> of a system, both in matrix form (with just numbers filling the matrices, because this is clearly a goofy question), how do I calculate the possible measured values of the energy of the system and more importantly, their probabilities? H is a 3x3 matrix and |phi> is naturally a 3x1 column vector.
I figure the possible measured values will just be the eigenvalues of the Hamiltonian (?), which I've calculated along with its eigenvectors, but now I'm really not sure how to get the probabilities, and I'm really not sure what to do with the state either. Anyone able to point me in the right direction?
e. nvm, got it
I don't really see how they can be "filled with numbers" without applying the operator?
[QUOTE=Killuah;39561004]I don't really see how they can be "filled with numbers" without applying the operator?[/QUOTE]
it's alright, I got it
I just had to find the overlap of the Hamiltonian eigenvectors and the state, that gives you the probability of the system being found in each state
I was going to suggest using Bloch-Sums to do a linear combination with the Eigenvectors
The probability density is defined as <Phi | Phi> so I think that's just multiplying the complex conjugate of Phi as a row vector with Phi as a column vector.
I'm not very familiar with QM though, only had an introductory course so far (part 2 is starting this semester)
Though that would just give you a number, I don't see how that's a PD. Maybe it's an exercise in working with the concepts of the matrix/vector representation?
F = m*g
Usually it's the integral over the absolute squared.
Gravitational force is for chumps pros use potential.
FP needs a latex plugin
Anyways, I just wrote a lab report for my second-year introduction to physical measurement course and I swear I've never been so ashamed of a couple pieces of paper in my life. There's only so much I can blame on human error...
For example, for the RLC circuit (ie. band-pass filter) that I made, I got
[img]http://puu.sh/21Hf6[/img]
through the equation
[img]http://puu.sh/21Hgo[/img]
and solving at A = 1.44.
:downs:
Where does the 276 come from?
I'm long out of that subject but from the graph it looks more like a difference of 17?
[QUOTE=Killuah;39572627]Where does the 276 come from?
I'm long out of that subject but from the graph it looks more like a difference of 17?[/QUOTE]
I think he means that he used the equation to solve A=1.44 and got 276kHz which he put on the graph to show how wrong he was
[QUOTE=Sobotnik;39478726]Found the paper I sat for physics: [URL]http://www.sqa.org.uk/pastpapers/papers/papers/2012/H_Physics_All_2012.pdf[/URL]
About the furthest I reached in physics. (And got a B, which is ok I guess)[/QUOTE]
oh man that was a fun paper. I remember being surprised they included an ion engine in it.
Anyway, to get myself involved in the chat, I'm currently doing Advanced Higher physics ( essentially first year uni physics ) as well as maths, and i've applied for and got unconditionals for Physics @ Glasgow Uni, Aberdeen Uni, Dundee Uni & Heriot-Watt ; I applied for computational physics at Edinburgh but i've not heard back from them yet.
I'm worried though as i'm starting to see the connection between chemistry and physics more and more, but i've not actually taken a single chemistry lesson. Damn.
and I should probably stop browsing FP as i've got a draft investigation to write-up
Chem isn't necessary for the majority of basic/intro physics. You'll use orbitals and the structure of the atom when doing quantization/nuclear/blackbody radiation/etc but bonding and everything related really isn't covered too much.
I would've loved to know the basics around Pi/Sigma bonds when I had that shit in Particle Physics.
There are two grad level relativistic quantum field theory courses and a grad level string theory course on MIT open courseware
I'm in love
I wish I was more profound in scientific english but since most of the Bachelor degree Physics stuff is German/European anyways there never was the need ...
[QUOTE=Killuah;39579169]I wish I was more profound in scientific english but since most of the Bachelor degree Physics stuff is German/European anyways there never was the need ...[/QUOTE]
Wishing won't get you anywhere, if you're interested enough the internet will suffice
regarding the "200% efficiency" LED thread that just got locked in SH: the LED is basically just acting like a tiny fridge, right?
[url=http://www.physicscentral.com/explore/action/led1.cfm]more info[/url]
Let's say I was travelling away from earth at nearly the speed of light. I decided my journey was going to be 2 hours (for me). I understand that on Earth, that 2 hours of mine would be significantly longer. Let's say a month or something. The math on that is probably way off but you see what I'm getting at here.
Now let's say I played a movie in my spaceship. Not just played it, but broadcast it back to Earth the whole time.
Would they see it in slow motion?
Extra credit for film critics who got lost: which movies would this improve?
No it would gradually get slower until the last picture arrives at 2*(whatever time passed outside) and DOA: The Movie
[QUOTE=Killuah;39584917]No it would gradually get slower until the last picture arrives at 2*(whatever time passed outside) and DOA: The Movie[/QUOTE]
So the distance alone would make it slower and slower but wouldn't time dilation mean it was slower from the very start as well?
How does exactly zero resistance with superconductors work? How does it interface with ohm's law?
if light from as far as 13.37 billion light years away can be seen from earth, that makes the light that we would be seeing representative of what that object looked like 13.37 billion years ago, right? how does that make sense, then, if 13.37 billion years ago the universe was a fraction of the size it is now? wouldn't the light have passed us if the universe used to be much smaller, and thus our solar system (or the point in space which eventually would become the location that our solar system right now exists in) used to be much, much closer to the source of the light? you know what i mean right?
yeah but the expansion has never slowed down, only sped up. i know it went fast, but i wouldn't think THAT fast...
[QUOTE=Yahnich;39593884]also this is wrong i just noticed, space expands as light travels so it would probably be closer to like 7 billion year old light (THIS IS COMPLETELY INACCURATE BUT U GET THE GIST RITE)
[editline]15th February 2013[/editline]
i also want to point out that stars and shit only started forming 150mil-1bil years after the big bang which gives it AMPLE of time to expand[/QUOTE]
the universe is about 13.75 billion years old, and the farthest observed proto galaxy is 13.37 billion light years away
are you sure that's ample time to expand enough?
[editline]15th February 2013[/editline]
in fact, according to the collective genius of wikipedia article creators/editors, that assertion about being closer to 7 billion year old light is incorrect (the article says "The actual stellar source of the light detected no longer exists.[10][11] The image is likely to correspond to a compact mini-galaxy[12] of blue stars that existed as we see it 13.37 billion years ago, around "380 million years"[2] after the Big Bang.")
Actually you can't see any further than ~300,000 years after the big bang, because light couldn't freely traverse space until that time. This light is observed in the CMB. We actually can't detect back to the big bang as far as I know.
[QUOTE=Falubii;39594104]Actually you can't see any further than ~300,000 years after the big bang, because light couldn't freely traverse space until that time. This light is observed in the CMB. We actually can't detect back to the big bang as far as I know.[/QUOTE]
read the article
[url]http://en.wikipedia.org/wiki/UDFj-39546284[/url]
[editline]15th February 2013[/editline]
anyway, this was, in theory, formed 380,000[B],000[/B] (wow) years after the big bang
[QUOTE=Falubii;39594104]Actually you can't see any further than ~300,000 years after the big bang, because light couldn't freely traverse space until that time. This light is observed in the CMB. We actually can't detect back to the big bang as far as I know.[/QUOTE]
yeah from what I remember is that there was so much energy in the beginning of the universe that hydrogen atoms were not able to form helium molecules so when you look back that far all you see is a wall of plasma which are the hydrogen atoms being forced not to bond.
[QUOTE=Goodthief;39594173]yeah from what I remember is that there was so much energy in the beginning of the universe that hydrogen atoms were not able to form helium molecules so when you look back that far all you see is a wall of plasma which are the hydrogen atoms being forced not to bond.[/QUOTE]
You're on the right track; the hydrogen atoms were all ionized and the free electrons trapped photons up until recombination when the hydrogen atoms became neutral again. They weren't making helium after recombination, just combining with electrons again.
[editline]14th February 2013[/editline]
[QUOTE=zzzz;39594138]read the article
[url]http://en.wikipedia.org/wiki/UDFj-39546284[/url]
[editline]15th February 2013[/editline]
anyway, this was, in theory, formed 380,000 years after the big bang[/QUOTE]
What am I looking for in the article?
i'm not sure, it sounded like you were trying to refute my point or something, but i guess you weren't since you said that the universe older than 300,000 years after the big bang could not be observed, but this was 380,000[B],000[/B] years after the big bang
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