someone plz explain me the very basics of quantum mechanics
>>7695017
discreetness
now read a fucking book
>>7695025
Wrong. Take your own advice. Why do highschoolfags with no knowledge of QM even comment on this thread?
Simultaneous states
>>7695017
The space of states is a vector space
Any state can be written as a linear combination of other states
Magic
>>7695017
Consciousness influences matter
>>7695017
Anything can happen at any time for no reason at all :^)
>>7695017
a mathematical analysis of the interactions of magnetic fields
>>7695017
DOUBLE PENETRATION
It's the topic in CS that studies the conditions necessary for quantum computing
Without quantum tunneling we wouldn't be alive.
>>7695383
Without lots of things we wouldn't be alive
>>7695082
lol
that waves sometimes act like particles and particles sometimes act like waves.
>>7695060
>The space of states is a vector space
I've never studied QM, and it's been ages since I studied physics of any kind, but I remember just enough for that to blow my fucking mind.
But I'm not sure why.
>Any state can be written as a linear combination of other states
This bit just makes sense. If it were divisible in a non-recursive way, it wouldn't be the smallest thing, now would it?
It spins, bro.
This should just about cover it.
[eqn]\left| {\psi \left( {x,t} \right)} \right\rangle \in \mathcal{H}[/eqn]
[eqn]i\hbar \frac{\partial }{{\partial t}}\left| {\psi \left( {x,t} \right)} \right\rangle = \hat H\left| {\psi \left( {x,t} \right)} \right\rangle [/eqn]
[eqn]\left\langle {x,t} \right.|\left. {\psi \left( {x,t} \right)} \right\rangle = \Psi \left( {x,t} \right)[/eqn]
[eqn] \int\limits_\mathbb{R} {{\Psi ^*}\Psi dx = 1} [/eqn]
[eqn] \left[ {x,p} \right] = i\hbar [/eqn]
[eqn]\left\langle {{x_f},{t_f}} \right.|\left. {{x_0},{t_0}} \right\rangle = \int {\left[ {Dx} \right]} \exp \left( {\frac{i}{\hbar }S\left[ \mathcal{L} \right]} \right)[/eqn]
curvy double-u = big E over h with a line through it
>>7695463
I like how you can remember the confusing pictures because the *i*-talic tridents are *ei*-genfunctions.
>>7695463
Psi as element of Hilbert space has no fucking dependency of x and t. That comes in when you project it. Holy shit elementary physics, newbz.
A particle can take different paths. Each of these paths has a strange type of probability associated with it that is like a wave.
These paths literally interfere with each other.
You can only observe one outcome despite this with probability calculated from these weird probabilities described earlier.
The rest is just peanuts calculations and weird stuff about the consequences of this.
>>7695501
Yes it does. [math]\left| \psi \right\rangle = \sum\limits_x {\Psi \left( x \right)\left| x \right\rangle } [/math] where the |x> are the basis of the Hilbert space.
>>7695526
>Not knowing what a projection is
>>7695526
no
please don't use the equals sign if you've no idea what it means.
>>7695463
Why not give the general form of the commutator instead of the result of a common one?
[math][\hat{A},\hat{B}]=\hat{A}\hat{B}-\hat{B}\hat{A}[/math]
Also I don't quite understand the third equation.
Isn't the LHS a scalar product using the bra-ket notation?
What is the difference between [math]\Psi[/math] and [math]\psi[/math]
>>7695065
Wrong, it's the other way around
>>7695712
It's pretty much tautological since consciousness is something that is really just a special arrangement of matter, so saying matter affects matter is not really interesting or remarkable.
