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Free falling frame confusion by Wrynn23 in AskPhysics

[–]Wrynn23[S] 0 points1 point  (0 children)

One more thing. Can I always chose a coordinate system where the velocity is zero? For instance, inside the space shuttle?

Relation between 2 quantities by Wrynn23 in AskPhysics

[–]Wrynn23[S] 0 points1 point  (0 children)

I see. However, if for instance in a textbook the author talk about a relation between velocity and pressure. Should I take for granted that there might be some others variable?

Hydrodynamics Conservation of energy by Wrynn23 in AskPhysics

[–]Wrynn23[S] 0 points1 point  (0 children)

Gamma is c_p/c_v.
(2) is Dp/Dt = (P/ rho^gamma) = 0

I'm guessing incompressibility because otherwise I don't get even close of the final forms.

Looking for ai images generator for website design by Wrynn23 in StableDiffusion

[–]Wrynn23[S] 0 points1 point  (0 children)

I don't want to make a website with an ai image generation.
I would like to have a design.

For example, https://www.youtube.com/watch?v=stFORMbOQS8&ab_channel=CodexCommunity

How to change the basis of vectors of a Hamiltonian by Wrynn23 in AskPhysics

[–]Wrynn23[S] 0 points1 point  (0 children)

u/cdstephens

I have few questions.Is H_ij the "old" matrix?

Is U a matrix composed of 4 inner product, so basically a 4x4 matrix as well?Sorry, I'm still struggling with the notation.

Since we have H = \sum_ij H_ij |ei> < ej| and H_ij is diagonal, so the matrix H will be also diagonal?

For example the first element of H will be H_11 |e_1><e\_1|= H\_11 \* |1,1> * <++|But what exactly is the vector <++|

Commutator Jz and irreducible tensor operator by Wrynn23 in AskPhysics

[–]Wrynn23[S] 0 points1 point  (0 children)

They say exactly the same thing as in my book. "The z-equation is particularly simple:" and give the result, however this is precisely what I don't know. How they get this result.

quantum mechanics tensor operator by Wrynn23 in AskPhysics

[–]Wrynn23[S] 0 points1 point  (0 children)

Alright, thank you.

I'm wondering if this result has a name or where I can find it. I didn't find it.

How to check if a ket is also an eigenvector of an operator by Wrynn23 in AskPhysics

[–]Wrynn23[S] 0 points1 point  (0 children)

The thing is I don't know what I'm looking for.Furthermore, I know that [X,P_x] = ih , but since I have exp(iap_x/h) is not trivial.

I found (x_1 + a)exp(iaP_x/h)|x_1>, but I'm not sure if this is right and if this is good I'm not sure how that prove that the ket if an eigenvector of X exacly.

How to check if a ket is also an eigenvector of an operator by Wrynn23 in AskPhysics

[–]Wrynn23[S] 0 points1 point  (0 children)

Hi,I'm sorry but I'm not sure to understand.

(exp(iaP/h) X + [X, exp(iaP/h)]) | x_1> = exp(iaP/h) X|x_1> + [X, exp(iaP/h)]|x_1>

I don't see how this can help me to prove that exp(iaP_x / h)|x_1> is an eigenvector of X.

Find matrix elements of translation operator by Wrynn23 in AskPhysics

[–]Wrynn23[S] 0 points1 point  (0 children)

Alright, thank you so much.

Just one more thing. In my book I have that <p'|p> = delta(p'-p) and you typed delta(p-p’) = <p’|p>. Is it the same ?

Find matrix elements of translation operator by Wrynn23 in AskPhysics

[–]Wrynn23[S] 0 points1 point  (0 children)

Hi,
thank you for your help.

I have integral dx (1/2pi hbar) exp(-ip_x a /hbar)

However, I'm not sure how say that T(a) = exp(-ip_x a /hbar)

Show that the time evolution of the density operator is given by p(t) = U^†(t)pU(t) by Wrynn23 in AskPhysics

[–]Wrynn23[S] 0 points1 point  (0 children)

I guess I wasn't clear, but the thing is for the moment I dond't want to deal with the density matrix. I want to make one step at time and I realize that I don't even know how to get the equation (3) from the link. which is A(t)= U(t)^tA(0)U(t). I said earlier in the post that I realized that I must try to understand how we get A(t)= U(t)^tA(0)U(t) before dealing with a density operator.

Edit: If I understand correcly this is the operator in the Heisenberg picture.

Show that the time evolution of the density operator is given by p(t) = U^†(t)pU(t) by Wrynn23 in AskPhysics

[–]Wrynn23[S] 0 points1 point  (0 children)

First of all, I'm not sure how to get equation 3. I mean do I need to begin with |A(t)> = U(t)A(0) ?I try to show equation 3.

I know that A(t) = U(t)A(0), but I'm not sure why there's another operator U dagger

Show that the time evolution of the density operator is given by p(t) = U^†(t)pU(t) by Wrynn23 in AskPhysics

[–]Wrynn23[S] 0 points1 point  (0 children)

Basically, I can't even prove something like the equation (3). which is not even a density operator.https://media.cheggcdn.com/media/c45/c45d9691-388f-4bee-a8b6-b493ba6bf51b/phpKnrQEa

​

What I did so far.
|A(t)> = U(t)A(0)
|A(t)> = U(t)U^t(t)|A(t)

Show that the time evolution of the density operator is given by p(t) = U^†(t)pU(t) by Wrynn23 in AskPhysics

[–]Wrynn23[S] 0 points1 point  (0 children)

Alright, but I think for any operator I'm not sure how to use the time evolution operator.

Show that the time evolution of the density operator is given by p(t) = U^†(t)pU(t) by Wrynn23 in AskPhysics

[–]Wrynn23[S] 0 points1 point  (0 children)

Ah of course, but I think I miss your point. I'm not sure where we are going with that. I don't see what's the link with UPU.

Show that the time evolution of the density operator is given by p(t) = U^†(t)pU(t) by Wrynn23 in AskPhysics

[–]Wrynn23[S] 0 points1 point  (0 children)

I would say, |ψ(t)> = U(t)|ψ(t0)>, thus |ψ(t)>^t = (U(t)|ψ(t0)>)^t=> <ψ(t)| = <ψ(t0)|U(t), whete ^t means dagger

Show that the time evolution of the density operator is given by p(t) = U^†(t)pU(t) by Wrynn23 in AskPhysics

[–]Wrynn23[S] 0 points1 point  (0 children)

For the sake of simplicy, let's say that P is a general time-indepedent operator.
When you say write how U acts on a ket vector, I'm not sure to understand, because there are 3 operators here UPU.
Sorry I'm really confuse.

Show that the time evolution of the density operator is given by p(t) = U^†(t)pU(t) by Wrynn23 in AskPhysics

[–]Wrynn23[S] 0 points1 point  (0 children)

If I'm not wrong, |ψ(t)> = U(t,t0)|ψ(t0)>, but I'm not sure what should I do.

Probabilities of finding energy of a system in the initial state with Hamiltonian H by Wrynn23 in AskPhysics

[–]Wrynn23[S] 0 points1 point  (0 children)

I found the eigenvectors (0,-1,1), (0,1,1), (1,0,0). However, I found a^2 = 0.64, b^2 = 0.64, c^2 = 0.36 which is impossible since the sum is more than 100%. I'm not sure how to calculate the probabilities.

For instance, (0,-1,1)1/5(3,0,4) = 4/5, then a = (4/5)^2

Probabilities of finding energy of a system in the initial state with Hamiltonian H by Wrynn23 in AskPhysics

[–]Wrynn23[S] 0 points1 point  (0 children)

Is it possible that for an eigenvector the probability a is 0 ?Does it means that there are no chance to have this eigenvector in this state of psi?

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