Recent content by IanBerkman

The magnetic field magnitude would be uniform along the circular ring coaxial with the dipole. However, the magnetic field vectors would be different along the ring. Let us consider the same magnetic dipole again in the y-direction, and we know the field at a certain position is of the form...

Hi all, Consider one has a magnetic dipole, the field given by: \begin{equation} \vec{B} = \frac{\mu_0}{4\pi}\left(\frac{3(\vec{m}\cdot\vec{r})\vec{r}}{r^5}-\frac{\vec{m}}{r^3}\right) \end{equation} where we can take $$\vec{m} = m\hat{y}$$. Let us say we have the a magnet vector which is...

I came to this part and found the solution to this integral somewhere, not knowing I had to use the "imaginary part" trick. I tried it on my own with this trick and got to the same conclusion. Thanks.

Dear all, In my quantum mechanics book it is stated that the Fourier transform of the Coulomb potential $$\frac{e^2}{4\pi\epsilon_0 r}$$ results in $$\frac{e^2}{\epsilon_0 q^2}$$ Where ##r## is the distance between the electrons and ##q## is the difference in wave vectors. What confuses me...

All right, thank you. You guys are great with helping!

All right, and is the following true? $$\nabla|\textbf{r}_1\rangle=\nabla_{\textbf{r}_1}|\textbf{r}_1\rangle$$

I forgot to mention my notation. I used ##\boldsymbol\sigma=(\sigma_x,\sigma_y,\sigma_z)##. Is this notation wrong?

Hm, I am stuck with another Hamiltonian at this moment. It is somewhat similar as the problem above so I will put it here (I could also make a new thread but I have been making too many lately :oldfrown:) I want to prove the following...

Hmm, the book talks about the direct product between more Hilbert spaces. I know how to "visualize" one Hilbert space i.e. a vector with eigenstates as orthogonal axes. However, is there also an intuitive way to visualize a Hilbert space which consists of the tensor product of two other Hilbert...

Any vector working on the Hamiltonian will result in another 2-dimensional vector where the first component responds to the spin-up ##(1, 0)^T## and the second to the spin-down state ##(0,1)^T##. Since the basis spanned by the eigenvectors of ##\sigma_z## is $$\left\{\begin{pmatrix} 1\\0...

Dear all, I know how to interpret a vector, inner product etcetera in one Hilbert space. However, I can not get my head around how the direct product of two (or more) Hilbert spaces can be interpreted. For instance, the Hilbert space ##W## of a larger system is spanned by the direct product of...

It is clear now, thank you.

.For a general function the answer is ##\nabla'f(x-x')=-\nabla f(x-x')##. I was too distracted with the delta function itself, this also explains the minus sign

Dear all, I have a quick question, is the following statement true? $$\nabla_\textbf{x'} \delta(\textbf{x}-\textbf{x'}) = \nabla_\textbf{x} \delta(\textbf{x}-\textbf{x'})?$$ I thought I have seen this somewhere before, but I could not remember where and why. I know the identity ##d/dx...

All right, thanks. I found it more convenient to work with ##U^\dagger## than with ##U^{-1}##.