Questions/Comments on Quantum Mechanics
Wed, Apr 16, 10:50 p.m. - Could you explain why the fluorescence appear after it absorb energy like from UV?
Sorry I didn't see this sooner. The key point of fluorescence is that an electron absorbs a high energy photon and takes a big step up, and then takes two or more steps back down, emitting smaller energy photons. So this picture requires at least three energy levels.
For example, the incoming photon might move the electron from level 1 to level 3. Then the electron drops down from level 3 to level 2 and emits a smaller energy photon. Then it drops from level 2 to level 1 and emits another smaller energy photon.
Wed, Apr 16, 2:18 p.m. - Is there a difference between $|\vec S|$, $S_z$, $m_s$ and $|\vec L|$, $L_z$, and $m_l$ or is it just different notation?
S and L both describe angular momentum, and so they have some of the strange rules of quantum mechanics, such as $m_s = -s, -s+1, \dots, s$ and $m_\ell = -\ell, -\ell+1, \dots, \ell$. But they are describing different sources of angular momentum: spin versus orbital angular momentum.
To use the solar system as an analogy: there is angular momentum in the Earth rotating about its axis, which is like the spin of the electron, and separately there is angular momentum in the Earth's revolution around the Sun, which is like the orbital angular momentum $L$.
Wed, Mar 19, 7:24 p.m. - Hey, I am wondering how we can determine j max? Does j max mean N is also maximum?
The number of photons in the $j$th mode goes as $1/j$. The larger $j$ gets, the smaller $N_j$ gets. But $N_j$ can't become smaller than 1, so this defines $j_\text{max}$: it's the value of $j$ at which $N_j=1$. That is, $N_{j_\text{max}}=1$.
So that is how you find $j_\text{max}$. For example, if you know $N_1=4500$, then we must have $N_j = 4500/j$ (notice that it gives the right answer for $j=1$). So now $N_{j_\text{max}} = 4500/j_\text{max} = 1$, which you can solve for $j_\text{max}$.
Wed, Mar 19, 7:21 p.m. - The question I would like to ask is in lecture 13, we learned about Eth = (0.5 kB T per mode)*(# of mode). By this formula, why can't we have infinite energy? Thanks!
The formula does predict infinite energy, but we know that this isn't what happens. Because if it did happen, we would all be cooked by the infinite EM wave thermal energy. But also, we can measure how much energy there is, and so it's a known quantity that is definitely not infinity.
What we learn from this is that the approach that led to $E_\text{th} = (0.5 k_BT \text{ per mode}) \times (\text{# of modes})$ must be wrong. It was based on assuming the EM waves were just waves and neglected the photon aspect of light. The solution is to not neglect that light is made up of photons.