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classes:2009:fall:phys4101.001:quiz_3_1113

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Important concepts covered in Quiz 3

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If the class contribute to this page, I would be happy to help by commenting on your contributions.

Andromeda 11/8 9:58

I think the two angular equations on page 136 (<math>\frac{1}{\Theta}\left[\sin\theta\frac{d}{d\theta}\left(\sin\theta\frac{d\Theta}{d\theta}\right)\right]+l(l+1)\sin^2\theta=m^2</math> and <math>\frac{1}{\Phi}\frac{d^2\Phi}{d\phi^2}=-m^2</math>) and the radial equation (<math>\frac{1}{R}\frac{d}{dr}\left(r^2\frac{dR}{dr}\right)-\frac{2mr^2}{\hbar^2}\left[V®-E\right]=l(l+1)</math>) are important since we can use them to find probabilities of finding a particle in a sphere. also since the wave function is a separable functions we should be able to find radial probability density and angular probability density; for example the probability of finding the particle in the volume between r and r+dr.I think for this reasons and the fact that quantum mechanics is all about probabilities, these three equations are of importance.

Andromeda 11/8 10:05

Also from chapter 3 i would put down equation 3.71(<math>\frac{d}{dt}\left<Q\right>=\frac{i}{\hbar}{\left<[\hat H,\hat Q]\right>+\left<\frac{\partial\hat Q}{\partial t}\right></math>). there was a few homework problem that we had to use this for.

Blackbox 11/8 12:00

I think, the equation 3.54 on page 108, the momentume space wave function might be important. <math>\displaystyle \Phi(p,t)= \frac1 sqrt{2\pi\hbar} \int exp(\frac{-ipx} {\hbar})\Psi(x,t) dx</math> We can use this equation to obtain the probability that a measurement of momentum would yield a value under a specific condition.

Blackbox 11/8 12:15

And also the position space wave function on page 108, <math>\displaystyle \Psi(x,t)= \frac1 sqrt{2\pi\hbar} \int exp(\frac{ipx} {\hbar})\Phi(p,t) dp</math> might be easily forgotten.

classes/2009/fall/phys4101.001/quiz_3_1113.1257704807.txt.gz · Last modified: 2009/11/08 12:26 by x500_sohnx020