Recent content by Lebnm

In the derivation of the Fermi-Dirac and Bose-Einstein distributions, we compute the Grand Partion Function ##Q##. With ##Q##, we can compute the espection value of the occupation number ##n_{l}##. This is the number of particles in the same energy level ##\varepsilon _{l}##. The book I am...

thank you!

Ok, I understood. Thank you guys!

If we have a system composed by two interacting particles, it's writeen in many textbooks (like "Quantum Physics", Le Bellac) that we can write the total Hilbert space ##\mathcal{H}## as the tensor product of he Hilbert spaces of the particles isoleted (##\mathcal{H}_{1}## and...

It was not exactly my question. Let me consider another exemple: A hydrogen atom. The hamiltonian is $$\hat{H} = \frac{\hat{P}_{p}}{2 m_{p}} + \frac{\hat{P}_{e}}{2 m_{e}} + V(\hat{r})$$If I take ##\mathcal{H}## to be ##\mathcal{H}_{p} \otimes \mathcal{H}_{e}##, where ##\mathcal{H}_{e(p)}## is...

I have a doubt about the definition of the kets of a composite system. If I understood correctly, when we have a composite system, that is, a system made of any number of subsystems (like two particle or a particle with spin), the Hilbert space ##H## of the total system will be the tensor...

Ok, thank you!

By the Wigner theorem, symmetries transformations are implemented by operators ##\hat{U}## that are unitary or antiunitary. This is what is written in most books. But I have read somewhere that, to ##\hat{U}## represent a symmetrie, it's necessary that ##\hat{U}^{\dagger} \hat{H} \hat{U} =...

I have two question about a exemple given in the Sakurai's quantum mechanics book, section 4.3. Let's consider an electron in a periodic potential ##V(x + a) = V(x)##, that has the form of a wave. We will take the potential to go to infinity between two latteces sites, such that its form change...

Why? Would not this imply that all potentials are local? Do you have references about this? it has been difficult find books that talk about this.

In quantum mechanics, I can write the hamiltonian as ##\hat{H} = \hat{p}^{2}/2m + \hat{V}##. I am confusing with the definition of the operator ##\hat{V}##, who represents the potential energy. If the potential energy depend only on the position, is it correct write ##\hat{V} = V(\hat{x})##...

If I have a composite system, like a two particle system, for exemple, I can construct my Hilbert space as the tensor product of the hilbert spaces of these particles, and, if ##\{|A;m \rangle \}## and ##\{|B;n \rangle \}## are basis in these hilbert spaces, a basis in the total hilbert space is...

Oh, it's true... I don't believe I have forgotten this haha. But my density matrix is incorret, isn't it? it couldn't have a imaginary factor multiplying an external product...

thank you!

I am studyng the deduction of Fermi-Dirac and Bose-Einstein distribution, but I'm not understanding one part. If we have a system of ##N## identical non-interaction particles, with energies levels ##\varepsilon _{l}## and occupation number ##n_{l}## (this is the number of particles with the same...