/sci/ - Science & Math

Bump

Non OP bump, as interested.

lol this isnt a thread about religion, fuck off OP!

>>3137866
Lol
fuck all this religious shit, we need some real science.

>Now, if one takes the derivative in double respect
im not familiar with this term, what do you mean?

Bumping

>>3137894
OP here.
Sorry about that, I use a lot of my own terms.
It just means you take two separate derivatives of one equation by different parameters. Sorry for the confusion.

Your topic sounds answer-worthy, but it's a pain in the ass to read.
Read the pic, use its contents and I'll give it a shot.

this isn't about my favorite politico economic system.

therefore sage

>dH/dp-dH/dq
>and this gives one the development of momentum with respect to the field and velocity.

you would have to define what dH/dp-dH/dq is supposed to be. for startert...the units dont match.
Btw., what "field"?
>My question is, if one takes the derivative, as shown above, of this equation, does one acquire the development of the wave function?
developement with respect to what? note time certainly, caus you only consider the stationairy schrödinger equation, not the full one. and in QM q and p are not seperate from each other in the way they are in classical mechanics.

testing

<span class="math">2^{2}[/spoiler]

>>3137840
>if one takes the derivative, as shown above, of this equation, does one acquire the development of the wave function?
The wavefunction is a field variable rather than a coordinate. To determine its evolution does not require derivatives if you have the energy and Hamiltonian operators.

>>3137920
OP here
Well, the equations needed are

<span class="math">\frac{d\mathbf{H}}{d\mathbf{q}}[/spoiler]

With that, and knowing the bottom is the Schrodinger equation, then you should be able to figure out the rest.

>>3137932
OP here.

If you examine the Schrodinger equation, you see the Potential operator which takes into account the field, of which, the quantum particle is in. However, for the purposes of a one dimesional particle, I can exclude it. Imagine the one d particle in box.

>>3137969
OP here.
Thanks, that's what I wanted to know.

So, the difference between classical and quantum (in this case) is the need to take the derivative of the hamiltonian on the state. One doesn't need to in QM.

>>3137965
Well since you didn't repost I'll just answer the last sentence.
>does one acquire the development of the wave function
No. <span class="math">H\psi=E\psi[/spoiler] is the time-independent Schrödinger equation. You'll get the time development by applying the time development operator, which is <span class="math">U=\exp(iHt)[/spoiler] to the state <span class="math">\psi[/spoiler].
The full Schrödinger equation is <span class="math">\mathrm i\partial_t\psi=H\psi[/spoiler]; this one still contains the time as a parameter.

>>3138013
OP
All right then, that makes sense. So, the E section is just the eigenvalue? Calculating, we are left with a complex development (as the Quantum Hamiltionian and time operator contain complex number).

>>3138035 the E section is just the eigenvalue
Yes, the time-independent Schrödinger equation is nothing but an eigenvalue equation. (Note that the Hamiltonian is self-adoint, so its eigenvalues are real; there are no complex energies coming out of that equation.)

Well, the eigenvalue is ih(bar)d/dt. This is complex, and the momentum of a quantum particle is complex.

Sorry for not using the system, it's late.

>>3138035
there is no continous section like H(p,q)=E, but a special set of basis vectors, namely the eigenstates of H, which correspond to a specific Energy value/frequency.

The state, let's call it S, is a composition of those eigenvectors and therefore a wild weighted ensemble of frequecies. Every eigenvector changes (in time) acording to his Energy/freqeuncy and if the eigenvectors change then S does too, because S is composed of them.

the seperate eigenvectors might be represented in a q-space or in the p-space, but they themself aren't really related to H anymore.

>>3138060
ich schick dir jetzt das pdf, k

>>3138078 Well, the eigenvalue is ih(bar)d/dt.
Nope. Eigenvalues take values in the field the vecor space is constructed upon. <span class="math">i\partial_t[/spoiler] isn't element of the field QM uses (<span class="math">\mathbb C[/spoiler]). The full Schrödinger equation isn't an eigenvalue equation.

>>3138078
Op here.
To correct myself, the momentum operator is complex.

>>3138092 ich schick dir jetzt das pdf, k
bin besoffen, heut abend musste nix tolles erwarten ;)

>>3138060
>the Hamiltonian is self-adoint, so its eigenvalues are real; there are no complex energies coming out of that equation.
>mfw authors using complex energy to determine the lifetimes of states fucking everywhere

>>3138103
scuse me?

>>3138099
ich will auch nicht, dass du's besoffen anschaust, oder im stress, oder wenn du auf 4chan rumgurkst - wenns bis nächstes WE angeschaut wär wärs cool

>>3138119
Is bisher nix angekommen

>>3138117
I'll dig up some examples. I'm pretty sure there are more, but I can't be bothered to trawl my collection right now.

http://pra.aps.org/abstract/PRA/v71/i2/e022703
http://prb.aps.org/abstract/PRB/v77/i24/e245426

>>3138173
Energy is measurable, and one of the postulates of quantum mechanics is that every observable is described by a self-adjoint operator, which has real eigenvalues.
I'll have a look at the papers you've posted when I'm in posession of my mind again, thanks for the links.

>>3138196
FWIW my underhanding is that complex energy is a typical concept in these approaches to quantum physics problems, and the statement is that when the imaginary part is zero you have a bound (integrable) state. Otherwise your state is non-integrable, and thus unbound. But I thought this meant the state could still exist, whereas the requirement that the energy is real would suggest it cannot.

>>3138229
Sounds like a mathematical trick that has nothing to do with reality to me, just like 5.5 dimensions and continuous (quantum mechanical) spin.

>>3138238
If you like mathematical tricks that just happen to work, you're gonna looooove that first paper I posted.

>>3138258
Sounds promising!

>>3138119
Rate mal wer vergessen hat wedge in den Betreff zu schreiben und daher eine Mail an meinen Müll geschrieben hat ;)
Gut dass ich da noch reingekuckt hab.

>>3138269
wedge? ist das nicht ein bischen ein random codewort

>>3138272
Es hält mir Spam vom Leib. Wie auch immer, hab das PDF bekommen.
Kommentare werd ich aber keine schreiben können, das is unter Linux irgendwie nur schwer bzw. ekelhaft möglich. Ne Textdatei sollt's aber tun ("auf seite 123 steht blabla da sollte foobar stehen")

>>3138293
>implying seite 123

>>3138308
Ich wollte sagen "Seite <span class="math">n[/spoiler] mit <span class="math">n\in\{1,\ldots,52\}[/spoiler]". Blödmann ;)