Quantum mechaincs Definition and 108 Threads

Homework Statement Find <r> and <r2> for an electron in the ground state of hydrogen. Express in terms of Bohr radius. Homework Equations We know the relevant wave functions are: R_{10} = \frac{c_0}{a}e^{r/a}Y^0_0 and Y^0_0 = \frac{1}{\sqrt{4\pi}} The Attempt at a Solution As I...

Hi , I finished my undergrad major in physics this fall. I wish to apply to grad school for next fall, so I need some book review books on physics, I n my university we followed Griffith's intro to QM as textbook, I solved almost all the problems there upto chapt 7, but this seemed a more...

I am at the very last part of a relatively long derivation of the Casimir effect, and I just don't understand the final step D: So far, I have derived the ground state energy to be \langle 0| \hat{H} |0\rangle = \delta (0) \int _{-\infty}^{\infty} dp \frac{1}{2} E And for a massless field...

Hello! I am reading about the creation and annihilation operators and I don't get how you find the creation operator from the annihilation one. The creation one is \hat{a}=\sqrt{\frac{m \omega}{2 \hbar}}\left( \hat{x}+\frac{i \hat{p}}{m \omega}\right) and the annihilation operator is...

I am looking at the derivation of the Heisenberg Uncertainty Principle presented here: http://socrates.berkeley.edu/~jemoore/p137a/uncertaintynotes.pdf and am confused about line (21)... I do not understand why AB and BA are complex conjugates of each other... (I'm still in high school so I...

Homework Statement Consider the case of an atom with two unpaired electrons, both of which are in s-orbitals. Write the full basis of angular momentum eigenstates representing the coupled and uncoupled representations Homework Equations l=r×p lx=ypz-zpy ly=zpx-xpz lz=xpy-ypx l+=lx+ily...

I've been having troubles resolving the Schödinger's time independent one-dimensional equation when you have a particle that goes from a zone with a constant potential to a zone with another constant potential, yet the potential is a continuos function of the form: $$ V(x)=\left\{...

Homework Statement A particle of mass ##m## is constrained to move between two concentric hard spheres of radii ##r = a## and ##r = b##. There is no potential between the spheres. Find the ground state energy and wave function. Homework Equations $$\frac{-\hbar^2}{2m} \frac{d^2 u}{dr^2} +...