I am confused with the fact of radiation pressure on Wiki and my homework solution. They are both arguing that the pressure produced by a ray of light to be reflected with incident angle θ and intensity I is:
$$\frac{2I\cos^2(\theta)}{c}$$
My thinking
We know that:
$$Ft=\Delta p$$
We see the...
How does it work? (The derivative rules of FT)
We look at $$F[x(t)]=\hat{x}(f)$$
$$\mathcal{l} \text{ is a distribution, with}\tilde{x}=tx(t)$$
$$\mathcal{F}[Dl(x)]=\mathcal{F}l'(x)=2\pi il(\mathcal{F}\tilde{x})=2\pi i \mathcal{F}l(\tilde{x})$$
Till here I fully understand. But next step...
$$\frac{\partial^2}{\partial t^2}u(x,t)=c^2\Delta u(\vec{x},t)\qquad \vec{x}\in \mathbb{R}^n$$
is known as the wave equation. It seems not very trivial, so is there any derivations or inspirations of it?
To solve this equation, we have to know the initial value and boundary conditions...
Thx. Still a problem with transition and life time.
And with which equations can we calculate the life time and transition probability? Time-dependent Schrodinger equation? But for time-dependent S equation, it seems that the system will never transit and just be in superposition forever.
How...
Now that, in bound state, the particles have quantized energy. So the system can only absorb certain kinds of photons. But why when I see the absorption graphic in books(x-axis is wavelength; y-axis is intensity, transmission percentage or sth), they are all continuous? They do have peaks...
So if the wave function collapses after measurement, if I measure it again, will I still get the same eigenstate 100%?
If we solve the time-dependent Schrodinger equation. After our measurement, will it be still time-dependent? But the "collapse" seems to make it into stationary state
Thanks, I understand! And I also feeling "bad" about measurement. How can my "eyeball" influences the system?
And if the wave function collapses after measurement, does the system stay the same state afterwards which means I measure it again, will I still get the same eigenstate 100%?
Thanks for your answer. I understand it, but my mean problem is: why the this two events are not mutually exclusive?
In my case, I wanted to calculate the event that electron appears in the interval e.g. (0,1). But the system is in superposition state which is superposed by to eigenstate A and...
First, we know for every wave function
$$p(x)=\psi(x)^*\psi(x)$$ indicates the probability density of a particle appearing at the point x.
So if we calculate $$P=\int _M p \text{d}x$$ this gives the probability of the particle appearing in the range M.
On the other side, I was thinking about...