Recent content by Haynes Kwon

When modeling stellar structure and formulating equation of states, I've seen various cases where you have to take into account whether the constituent gas of a star is degenerate or not. But how do you determine if the gas is degenerate or not?

Why do we see more absorption lines in stellar spectra than emission lines?

Is commutator being zero for two operators the same statement as the two observables are compatible?

I know ##[x,p]## is not zero, so this could be the counter example. But is there any way to generalize this proof?

$$(AB)^+ = B^+A^+ = BA $$ since A and B are Hermitian operators. Now I have to prove the commutator ##[A,B] = AB - BA## may be non-zero. I will try to compute ##[A,B]<\Psi|\Phi>##

Definition of Hermicity is $$<\Psi|A|\Phi> = <\Psi|A\Phi> = <A\Psi|\Phi>$$ so, $$A^+ = A $$ Taking the Hermitian conjugate of a product AB yields ##B^+A^+##. If I cannot assume that the two wavefunctions are not eignvectors of A,B, how should I approach this proof?

Trying to prove Hermiticity of the operator AB is not guaranteed with Hermitian operators A and B and this is what I got: $$<\Psi|AB|\Phi> = <\Psi|AB\Phi> = ab<\Psi|\Phi>=<B^+A^+\Psi|\Phi>=<BA\Psi|\Phi>=b^*a^*<\Psi|\Phi>$$ but since A and B are Hermitian eigenvalues a and b are real, Therefore...

Let's look at the Boltzmann equation $$ \frac {p_{i}} {p_{j}} = e^{\frac{E_{j}-E_{i}} {kT}},$$ and take infinitely high temperature, the RHS becomes 1. I interpreted that this means every energy level is occupied by equal number of electrons. But if T is high enough, wouldn't the hydrogen atom...

In Bransden textbook, it is stated that the probability current density is constant since we are dealing with 1-d stationary states. It gives probability flux outside the finite potential barrier which I verified to be constant with respect to x, but it doesn't provide the probability current...

Given that the wave function represented in momentum space is a Fourier transform of the wave function in configuration space, is the conjugate of the wave function in p-space is the conjugate of the whole transformation integral?

Born's postulate suggests if a particle is described a wave function ψ(r,t) the probability of finding the particle at a certain point is ψ*ψ. How does this work and why?

Thank you very much.

Thank you all. May I ask one more? I don't see why this is not nuclear fusion.

Is α-decay same as nuclear fission? What is the difference?

Hi. Getting straight to the point, what is the difference between electrical potential energy and electric potential? Please be as specific as you can. Thank you.