Have I done this much right? I think I might have made a mistake because I was expecting the contribution to the expectation coming from the kinetic energy to vanish.
Suppose I have a system of N identical bosons interacting via pairwise potential V(\vec{x} - \vec{x}').
I want to show that the expectation of the Hamiltonian in the non-interacting ground state is
\frac{N(N-1)}{2\mathcal{V}}\widetilde{V}(0)
where
\widetilde{V}(q) = \int d^3 \vec{x}...
Do analysis.
I have the same interests as you and I would say that in retrospect taking algebra over analysis was a bad decision. Yes, lie groups and lie algebras play an important role in advanced theoretical physics like particle theory, but you won't be covering that; just finite group...
Any two-level system can be written in the form e^{-i\phi/2}\cos(\theta/2) | 0 \rangle + \sin\theta(\theta/2) e^{i\phi/2}|1\rangle justifying the Bloch sphere interpretation.
The density operator of the two-level system can be expanded in the basis of Pauli matrices...
Hi all,
Can anybody please explain to me the connection between Rabi oscillations and spin-1/2 systems?
I believe the connection lies in the bloch sphere and the ability to represent the spin-1/2 system by a superposition of Pauli matrices but I'm just not getting it.
Thanks
I suppose what I want to show is that the term
\sum_{\vec{k},\vec{k}',\alpha,\alpha'}\int d^3 \vec{x} c^\ast_{\vec{k}'\alpha'}c_{\vec{k}\alpha} (\vec{k}\cdot \vec{u}^\ast_{\vec{k}'\alpha'})(\vec{k'}\cdot \vec{u}_{\vec{k}\alpha})
vanihses. For then,
\frac{1}{2}\int d^3...
I'm trying to get from the magnetic vector potential
\vec{A}(\vec{x},t) = \frac{1}{\sqrt{\mathcal{V}}}\sum_{\vec{k},\alpha=1,2}(c_{\vec{k}\alpha}(t) \vec{u}_{\vec{k}\alpha}(\vec{x}) + c.c.)
where
c_{\vec{k}\alpha}(t) = c_{\vec{k}\alpha}(0) e^{-i\omega_{\vec{k}\alpha}t}...
What material do they cover and what are your interests.
Personally, I majored in physics/mathematics and took algebra over analysis.
The main use of analysis in physics is probably residue calculus which I taught myself when I needed it.
Hi all,
If I have the wave function of a system, then the expectation of position is easily visualized as the centroid of the distribution.
Does anyone know how to visualize the expectation of velocity given just the postion-space wavefunction (real and imaginary parts)
Homework Statement
An +x-polarized electron beam is subjected to magnetic field in the y-direction. What is the probablity of measuring spin +x after a period of time t.
Homework Equations
Time evolution operator U = e^{-i/\hbar \hat{H} t}
The Attempt at a Solution
Since the...
Hi all,
Consider the the number of distinct permutations of a collection of N objects having multiplicities n_1,\ldots,n_k. Call this F.
Now arrange the same collection of objects into k bins, sorted by type. Consider the set of permutations such that the contents of any one bin after...
I'm trying to evaluate the expectation of position and momentum of
\exp\left(\xi (\hat{a}^2 - \hat{a}^\dag^2)/2\right) e^{-|\alpha|^2} \sum_{n=0}^\infty \frac{\alpha^n}{\sqrt{n!}} |n\rangle}
where \hat{a},\hat{a}^\dag are the anihilation/creation operators respectively.
Recall \hat{x}...
Conservation of energy eh? I like that explanation.
What assurance do we have that the photon does not exchange energy with its surroundings in passing from one medium to another?
Is it it possible to `bump up' the energy of a photon that is part of a self-propagating electromagnetic...
This is something I really should know but found I was unable to explain it to myself. When a ray of light passes from one medium to another its frequency remains invariant, but it slows down, forcing the wavelength to decrease according to c = \nu\lambda.
The frequency of the wave will...
Thanks for replying.
How do you define x',p' etc.? You also say that i[H,X] is simply related to i[H',x] which is indeed easy to compute. In fact
i[H',x] = \frac{c^2\vec{p}}{E}
I'm afraid I don't say what the simply relationship is? Could you please expand upon that?