# Search results for query: *

1. ### A Cluster Decomposition.Vanishing of the connected part of the S matrix.

I disagree, because translational invariance tells us that if all coordinates go to infinity together the S matrix should be invariant. I think I solved the problem yesterday, when you integrate expression (with this 3-spacial delta) 4.3.8 the exponentials become "coupled" i.e. if you integrate...
2. ### A Cluster Decomposition.Vanishing of the connected part of the S matrix.

Im following Weinberg's QFT volume I and I am tying to show that the following equation vanishes at large spatial distance of the possible particle clusters (pg 181 eq 4.3.8): S_{x_1'x_2'... , x_1 x_2}^C = \int d^3p_1' d^3p_2'...d^3p_1d^3p_2...S_{p_1'p_2'... , p_1 p_2}^C \times e^{i p_1' ...
3. ### A Rigorous transition from discrete to continuous basis

Thank you so much man, that really helps and now my summer is going to be way more interesting!
4. ### A Rigorous transition from discrete to continuous basis

Hi all, I'm trying to find a mathematical way of showing that given a complete set $$\left |a_i\right \rangle_{i=1}^{i=dim(H)}∈H$$ together with the usual property of \left |\psi\right \rangle = ∑_i \left \langle a_i\right|\left |\psi\right \rangle\left |a_i\right \rangle ∀ \left...
5. ### Simulating quantum coefficients

Hi everyone, I want to generate 8 random variables (in reality to form 4 complex numbers) such that the sum of the 8 variables squared is equal to unity. The aim of generating such numbers is to perform a quantum simulation of 4 qubits (thus the 8 parameters). I've been trying to use...
6. ### I Density of States -- alternative derivation

Thank you so much! Could you explain how this is done in n-space, (I can't really picture k-space) or perhaps refer to a book that does that, I am struggling to find any alternative derivation! Thanks in advance! :)
7. ### I Density of States -- alternative derivation

I am trying to understand the derivation for the DOS, I get stuck when they introduce k-space. Why is it necessary to introduce k-space? Why is the DOS related to k-space? Perhaps if someone could come up to a slightly different derivation (any dimensions will do) that would help. My doubt ELI5...
8. ### I Physical interpretation of a Hamiltonian with a constraint

Dear physics forums, What is the physical interpretation of imposing the following constrain on a Hamiltonian: Tr(\hat H^2)=2\omega ^2 where \omega is a given constant. I am not very familiar with why is the trace of the hamiltonian there. Thanks in advance, Alex
9. ### I Fubini-Study metric of pure states

Okay, I first let you know my original attempt to comment on my procedure: Let dist(\psi,\phi) = || \psi - \phi || = \sqrt{ < \phi, \phi> + < \psi, \psi> - 2 || < \psi, \phi> ||} which is a metric. now dl = dist(\psi+d\psi,\phi) = \sqrt{ < \phi, \phi> + < \psi +...
10. ### I Fubini-Study metric of pure states

Okay,I think I just proved that (even though its not Fubini-Study metric) || |\psi>-|\phi> || is a metric aswell, as it satisfies d(x,y)≥0 , d(x,y)=0 ↔ x=y, d(x,y)=d(y,x) & d(x,z)...etc. is this the case? or have I made a mistake?
11. ### I Fubini-Study metric of pure states

Okay I see now what you mean now, yeah I agree it's quite confusing the notation. Either way I would be very grateful if you could give me a hand with this derivation by quicking off with the first steps please! Thanks beforehand!
12. ### I Fubini-Study metric of pure states

But why then is it called the distance between those two points? I think I know what you are saying: take the inner product and solve for the angle, then you get the arccos, but in the article I sent it was referred as the length. Moreover the ultimate aim of doing this is to derive the ds...
13. ### I Fubini-Study metric of pure states

Hello PF! I was reading https://en.wikipedia.org/wiki/Fubini–Study_metric (qm section like always :wink:) And can't figure out how to derive: \gamma (\psi , \phi) = arccos \sqrt{\frac{<\psi|\phi><\phi|\psi>}{<\psi|\psi><\phi|\phi>}} I started with \gamma (\psi , \phi) =|| |\psi> - |\phi>||=...
14. ### Help on Theoretical Physics Master's Application

I'm very interested in quantum mechanics and electromagnetism so I guess QFT could be my cup of tea, and definitely this is exactly one of the branches you can choose in this uni I'm applying...
15. ### Help on Theoretical Physics Master's Application

Hi everyone! I am currently in the process of applying for a masters degree in theoretical physics. I am having troubles on writing the personal statement part since I really need to make it shine (200 applications and 20 places:frown:) . Any definitely do's and dont's I should bear in mind? A...
16. ### I Principle of superposition of states

So for a complete description of a two-electron system one can say that the most general form is: |\Psi\rangle = \alpha|u\rangle |d\rangle + \beta|d\rangle |u\rangle + \gamma|u\rangle |u\rangle + \delta|d\rangle |d\rangle
17. ### I Principle of superposition of states

You absolutely hit the right spot, thank you so much! Sorry for being a pest <3
18. ### I Principle of superposition of states

Yes, but you guys must understand that up until the point where I was quoting Landau´s (when I wrote the question) he had not said anything about all that mathematical formalim you guys are stating, so I guess my question is more basic than all that?
19. ### I Principle of superposition of states

So let me get this straight, a system composed of two other states is simply the linear superposition of them both whereas two different systems with states |A> & |B> form the together system in the state |A>|B>?
20. ### I Principle of superposition of states

I don't see how they are different
21. ### I Principle of superposition of states

Upon reading Landau QM, the Principle of superposition of states, I got confused. It states (and i quote): "Suppose that, in a state with wave function Ψ1(q), some measurement leads with certainty to a definite result 1, while in a state with Ψ2(q) it leads to a different result 2. Then it is...
22. ### Help with Python modelling of a particle in a 2D box

Hello guys, I programmed a physics simulation where a particle with some initial conditions bounces off the walls of a 2d container. The simulation also includes gravity in the y-coordinates. The aim of the project is to produce a visual animation and further on include more particles and...
23. ### How to find a constant in this quadratic equation?

Hello! please use latex next time thanks! 1) Let x1=sin(θ) and x2=cos(θ), then by substitution into the original equation you can find the value of k since you are given the interval of θ. 2) I am not sure what is meant by the "constant term" but I will asume is (x^3+ \frac{a}{x^2})^5=-270...

Could somebody explain me why it would not be sufficient for a radio receiver of an AM signal to simply consist in two elements: A very long antenna. A speaker/headphones. The set up would be as follows, the antenna is connected to the speaker and the other part of the speaker is grounded. My...
25. ### I Help a novice with EL equation derivation

Thanks BvU! Any ideas on how to do this and why is it relevant?
26. ### I Help a novice with EL equation derivation

Hello everyone, Reading Landau and Lifshitz Course of Theoretical Physics Volume 1: Mechanics (page 3) I got suck in the following step (and I cite in italics): The change in S when q is replaced by q+δq is \int_{t_1}^{t_2} L(q+δq, \dot q +δ\dot q, t)dt - \int_{t_1}^{t_2} L(q, \dot q, t)dt...
27. ### A brief question on quantum thermodinamics.

And would that energy transformation be done without any energy lost in the process of transformation? Thanks for all the answers so far!
28. ### A brief question on quantum thermodinamics.

Hi, I am new to this forum so I don't really know if this question already exists.. My question is: When an electron absorbs a foton and climbs to the next energy gap and then returns again, as the energy is quantum energy, how is possible that the foton reemited by the electron has the same...