sup /sci/ atm im writing some shit for school, and i need to describe von neumanns intervention, se pic. What does it excatly describe? I have a good idea but im not totally sure.
Thx man
Tell us about your good idea.
>>7701043
>Tell us about your good idea.
Alright, so PSI tells us the wave function. Its dependent on what number "n" is, and "n" describes a position an atom can have. Cn is dependent on n aswell, as Cn describes how high chance the "n"-state has to be taken, after the Atom's superposition colapses. Lets consinder that the superposition of the atom already colapsed, therefore the wavefunction also colapses, because the function no longer is a function but a number. Because its mearly a number its described as ni.
Sry for bad english, its not my native language, and on this level of science its hard to explain in any other language than my own.
>>7701077
Did you mean
[eqn]\left\vert n \right\rangle [/eqn] is a stationary state.
[eqn]\vert C_n \vert ^2[/eqn] gives the probability to find particle in state [math]n[/math]
and [eqn]\left \vert \psi \right\rangle[/eqn] is a superposition of all stationary states?
>>7701090
and I probably meant state
[math]\left\vert n_i \right\rbrace[/math]
>>7701090
n is a possible outcome when a superposition colapses. Lets say there is 2 outcomes, then n becomes both 1 and 2, therefore the Ket Notation.
Cn is the same as alpha. http://www.umsl.edu/~snb2q4/qc/qcc.html
^read under Bra Ket notaiton, alpha is given.
If the probability of the outcome is 50/50 (50% for 1 and 50% for 2) Cn would be: Cn=1/root(2), because Cn^2 is 0.5 then.
ni is a stationary state. Its the outcome when the superposition colpases.
>>7701090
So you're probably right, im not sure about PSI tho.
>>7701120
I think i understand it now. PSI is like a function, a wave function like this picture i made. You can see n as the x-line (i dont know the word for it). as mentioned n represents the possible positions the atom can have in superposition. Then the y-line is the possiblity of exactly the n position of happening?
"sandsynlighed" is the same as posibility.
>>7701134
[math]\vert n \rangle [/math] represents a [b]state[/b] of the particle, not its position.
[math]\vert \vert n(x) \rangle \vert ^2[/math] represents the probability of finding the particle, which is in state [math]\vert n \rangle [/math], at location x.
>>7701166
Your picture is a probability density plot for a particle. On the x-axis you have the location, and on the y-axis you have the probability for the particle to be found —upon measurement— at location x.
>>7701166
With position i mean state, sorry.
Yes and isnt this what PSI represents?
>>7701172
Yup i am aware of that. I wanted to show that when u measure it, your force it to take 1 position as shown:
>>7701186
[math]\vert \Psi \rangle[/math] can be represented as a superposition of all [math]\vert n \rangle[/math].
[eqn]
\vert \Psi \rangle = \sum\limits_n c_n \vert n \rangle
[/eqn], like in OP pic.
If you prepare the particle in state [math]\vert \Psi \rangle[/math], then [math]\vert \vert \Psi (x) \rangle \vert ^2 [/math] again gives you the probability to discover the particle at point [math]x[/math]. Upon measurement the wave function collapses to state [math]\vert n_i \rangle [/math] with [math]\vert c_{n_i}\vert ^2[/math] giving the probability for the particle to collapse to state [math]\vert n_i \rangle [/math].
I may have missed the point of your question about what [math]\vert Psi \rangle [/math] represents. However, note that [math]\vert Psi \rangle [/math] and [math]\vert \vert Psi \rangle \vert ^2 [/math] are not the same. First is the wave function, the other is the probability density, acquired by taking the inner product of the wavefunction with itself.
>>7701207
thx man it makes sense now.
>>7701207
Question: n is a state right? Then the probability of this state is is determined by cn right?
>>7701374
Cn^2 i mean, and PSI just shows the different states it can take, since its a superposition of all states n can have?
>>7701207
And would PSI(n)^2 be the probability of the atom to take a certain state?
>>7701384
Or just PSI^2, because PSI is already dependent on n?
b
