# Search results for query: *

1. ### I How to obtain the determinant of the Curl in cylindrical coordinates?

The del operator is not a vector that crosses with vectors, although it resembles the property of vectors. I am sorry I am not an expert who can explain clearly to you about it, but here is a derive of the curl in other...
2. ### I How to obtain the determinant of the Curl in cylindrical coordinates?

The general formula for cylindrical coordinate is as follows: $$\vec{\nabla} \times \vec{V} = \frac{1}{r}\begin{vmatrix} \hat{r}\ & r\hat{\theta} & \hat{z} \\ \partial/\partial r & \partial/\partial \theta & \partial/\partial z \\ V_{r} & V_{\theta} & V_{z} \end{vmatrix}$$ Because ##V_r## and...
3. ### How to solve this 2nd order ODE?

I am sorry. I thought the approximation only refers to ##\frac{d^2\psi}{d\xi^2} \approx \xi^2\psi##; with regards to the approximation ##\frac{d^2\psi}{d\xi^2} \approx \xi^2\psi## , the following ##\psi = Ae^{-\frac{\xi^2}{2}}+ Be^{\frac{\xi^2}{2}}## is exact and is not an approximation.
4. ### How to solve this 2nd order ODE?

By the way, it would be very nice if you could explain what asymptotic form is in the second picture. I don't understand the transition from ##\psi = Ae^{\frac{-\xi^2}{2}}+Be^{\frac{\xi^2}{2}}## to ##\psi = h(\xi)e^{\frac{-\xi^2}{2}}##

6. ### How to solve this 2nd order ODE?

The solution is same as I stated. Actually this is from a proof on my textbook on quantum mechanics, where the proof is about solving the simple harmonic oscillator. ##\psi(x)## refers to the wave function; ##\xi## refers to the constant ##\sqrt{\frac{m\omega}{\hbar}}x##
7. ### How to solve this 2nd order ODE?

This is a very simple question: I would like to solve for ##\psi## in this equation $$\frac{d^{2}\psi}{d\xi^2} =\xi^2\psi$$ I so apply ##y=c_{1}e^{-kx}+c_{2}e^{kx}## and ##\psi## should be equal to ##\psi=c_{1}e^{-\xi^2}+c_{2}e^{\xi^2}##, because ##(D^2-\xi^2)\psi=0##. However the answer is...
8. ### I The derivative of the complex conjugate of the wave function

At least the transform covered in the Boas book...
9. ### I The derivative of the complex conjugate of the wave function

Yes, I have found the online version of your book. I will work through it later because I have just finished the Fourier series and transform. The problem of Hong Kong's educational system is not at the university level, but at the secondary school level. At secondary school, except for a few...
10. ### I The derivative of the complex conjugate of the wave function

By the way, where did you guys learn these from during your ug level study? Did you guys actually take a math course on complex analysis?

19. ### I How to interpret integration by parts

By the way, the poet is David J. Griffiths :)
20. ### I How to interpret integration by parts

A very silly question: when performing the integration wrt to dx, we keep the variable in ##\Psi## constant, right? Sorry but I am not very familiar with such type of multivariable integration.

40. ### Bound charge question

The Laplace's equation ##\nabla ^{2} V =0##, has the following solution in spherical coordinates: $$V = \sum_{l=0}^{\infty} (A_l r^l + \frac{B_l}{r^{l+1})P_{l}(cos\theta)$$. The potential boundary condition can be calculated by letting ##V_{in} = V_{out}##. But I don't know as well how you...
41. ### Bound charge question

This is an example of Griffith's book on bound charge, and the following is the solution to this example. We choose the z-axis to conincide with the direction of polarization. By $$\sigma_b \equiv \mathbf P \cdot \hat {\mathbf n}$$ and $$\rho_b \equiv - \nabla \cdot \mathbf P$$ we can...
42. ### Electric field of a polarized atom

I suppose we can treat the electron cloud as a point charge, just like what we do for centre of mass? If that's not the case, why would the author draw two points inside the sphere?
43. ### Electric field of a polarized atom

The question is like this: The solution is like this: However, according to the equation for ##E_{dip}## , what I think is that it should be: $$E=\frac {1}{4 \pi \epsilon_o} \frac {qd}{d^3} \hat {\mathbf z}$$, where I take the centre of the sphere in figure 2 as the centre of the...
44. ### What is the meaning of r' in the Multipole Expansion?

My poor English, that's what I want to say.
45. ### What is the meaning of r' in the Multipole Expansion?

I think ##\vec r## refers to the direction of the radial distance of the potential at a general point from the centre of the coordinate system, whereas ##\vec r^{'}## is the direction from the centre of the coordinate system to the infinitesmal charge; the angle between them is ##\alpha##, which...
46. ### What is the meaning of r' in the Multipole Expansion?

Then what is ##r##?
47. ### What is the meaning of r' in the Multipole Expansion?

The diagram of the problem should look something like this: ,which is just the normal spherical coordinate. To calculate the potential far away, we use the multipole expansion. ##I_o## in the expansion is ok, because ##(r^{'})^{0} = 1##. However, I am wondering how I should calculate...
48. ### The potential of a sphere with opposite hemisphere charge densities

Nice explanation!
49. ### The potential of a sphere with opposite hemisphere charge densities

This is hard but I will make a guess. I think for even numbers of ##l## the Legendre polynomials are tossed. The ##V_{out}## is given by: $$\sum_{l=0}^{\infty}\frac{B_l}{r^{l+1}}P_l(cos\theta)$$ For the first few ##l##s, \frac{B_1}{r^2} + \frac{B_2}{r^3}cos\theta +...
50. ### Can anyone help check where I went wrong (Potential of electrodynamics)?

Thanks. Your explanation is super clear.