Below is a scenario where at every step, you are choosing the more favourable option, but yet you would end up worse off definitely. How could it be?
Suppose you start playing a fair game (or a game slightly to your advantage) with $10 and bet $1 each round. You tell yourself that you would...
So non-relativistic QM and relativistic QM give different predictions even when the particle is not moving at relativistic speeds? I thought their predictions would agree at low speeds.
Anyway, for what really happens in the real world, there would be a "light-speed time lag" (in the particle's...
Suppose a particle is in an enclosed box for 10 seconds. At the 10th second (t=10s), the right wall of the box is removed. Suppose it takes 5s for light to travel from the right wall to the particle.
Then for the period between t=10s and t=15s, if we want to get the particle’s position...
Suppose I measured it and it now has a definite position. Then the environment changes.
Would the wave function change instantly? Or does it take some time for the wave function to change (eg, the time for light to reach the particle from the location of the environmental change)?
Suppose we have in a box a particle that is travelling left and right at some speed, bouncing off the walls of the box. The wall on the right is then removed such that the particle would be free to escape the box.
Does the wave function of the particle get "updated" instantly the moment the...
I am now studying quantum mechanics. Cosmology, not much, just read a bit here and there. I've watched Leonard Susskind's lectures on cosmology, but that was quite some time ago. Do you have a good resource to recommend that is related to my question?
Does cosmological event horizon radiate until it is completely gone too? Black holes can do that because they can shrink until they vanish. But for cosmological event horizon, the "hole" is outside of the spherical surface that is the event horizon (and we are inside the sphere). So I cannot...
I see. Then how does Hawking radiation come into play? Does a particle just move closer and closer to the horizon until one day it just disappears and is re-emitted instantly from another region (that is very close to the horizon)? And it's emitted with a velocity different from its original...
When objects/galaxies (particles and antiparticles) move across the cosmological event horizon, do they leave behind an “image” on the horizon, such that when we look at the image, we can tell what kinds of objects went through to the other side (ie, we would know information such as the mass...
I've seen the hydrogen electron's wavefunction expressed in the basis ##\ket{n l s m_l m_s}## or ##\ket{n l s j m_j}##, but so far, never in ##\ket{n l s m_l m_j}##. My question is, are certain combinations of quantum numbers, eg, ##\ket{n l s m_l m_j}##, forbidden?
If ##\ket{n l s m_l m_j}##...
This is the remaining part of the section in the book:
From the sentence below [6.81], we can see that eigenstates of ##S_z## and ##L_z## were used as the "good" states ##\ket{nlm_lm_s}## in the perturbation theory in [6.80].
So my question is, aren't eigenstates of ##J_z## "good" states too...
This textbook claims ##m_j## is not a "good" quantum number because the total angular momentum (of an electron of a hydrogen atom placed in a strong uniform magnetic field) is not conserved. I don't understand why ##m_j## is not a "good" quantum number.
Since ##J=L+S##, ##J_z=L_z+S_z##.
Since...
But how do you know that the "cross terms" are zero?
Suppose a good state ##\psi^{0}=\alpha\psi_{a}+\beta\psi_{b}## , where ##\psi_{a}## and ##\psi_{b}## are some ##\psi_{nlm}## .
##\braket{\frac{1}{r^3}}=\braket{\alpha\psi_{a}+\beta\psi_{b}|\frac{1}{r^3}|\alpha\psi_{a}+\beta\psi_{b}}##...