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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.

Can 11/9/09 1:21pm

I think the matrix operators of H and P we did in discussion are worth for the reviews. Especially how to find eigenvalues ,which corresponds to the energy and probility and eigenvectors, which corresponds to the eigenstate of wave function.

prest121 11/9/2009 8:50pm

I agree with Can about the discussion problem. Also, I think the Schwarz inequality may be useful, I know it has been used a few times in derivations in the book. Presently, it's important for the derivation of the general uncertainty principle. Here is the Schwarz inequality:

<math>\mid\int_{a}^{b}f(x)*g(x)dx\mid\leq\sqrt{\int_{a}^{b}\mid f(x)\mid^2 dx \int_{a}^{b} \mid g(x) \mid^2 dx}</math>

classes/2009/fall/phys4101.001/quiz_3_1113.1257821797.txt.gz · Last modified: 2009/11/09 20:56 by prestegard