Recent content by Tony Hau

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...

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...

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.

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}}##

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##

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...

At least the transform covered in the Boas book...

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...

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?

$$(\frac {\partial \psi} {\partial t})^* = (\frac {\partial \psi_{1}} {\partial t} + i \frac {\partial \psi_2} {\partial t})^* $$ $$=(\frac {\partial \psi_{1}} {\partial t})^* + ( i \frac {\partial \psi_2} {\partial t})^*$$ $$=\frac {\partial \psi_{1}} {\partial t} - i\frac {\partial \psi_2}...

That's easy. $$ (e^{i\theta_1}\cdot e^{i\theta_2})^* = (e^{i(\theta_1 +\theta_2)})^*$$ $$= e^{-i(\theta_1 +\theta_2)}$$ $$=e^{-i\theta_1}\cdot e^{-i\theta_2}$$ $$=e^{i\theta_1*} \cdot e^{i\theta_2 *}$$ What really surprises me is the complex conjugate on the partial derivatives.

Thanks for your hints. That's much much better. Honestly I don't know what it means by learning complex number. I have taken a course(maths for physics student I, you can say) where I was taught the Euler's formula, the complex equation for natural logarithm, sine and cosine. But obviously I...

I have asked one of my frds from math department and obtained the following proof. Forgive me for uploading only two piece of paper because I would like to spare my effort in typing latex. . I do not understand why taking the complex conjugate seems so intuitive and obvious to you guys.

Good idea. You know my school's education sucks. It even doesn't teach Fourier Series and Fourier transform, which I am self-learning during this winter break. I am using the Mathematical methods for physical science of Boas, which my school uses for teaching ODEs.