Recent content by v0id

Thanks, I had never heard of Dirac's book until now. By "complete", I mean self-contained, so the reader does not have to refer to external sources due to the author imprecisely glossing over important topics. Landau, Shankar and Ballentine are complete/comprehensive. Griffiths, Scherrer and...

I've searched high and low for a terse (yet complete) introduction to the foundations of non-relativistic QM. Shankar is unparalleled in terms of completeness, yet it is infuriatingly verbose. Landau's presentation is a bit dated and difficult to follow in many instances. It is also not as...

Math is indeed hard, mathwonk. I suppose one cannot substitute for intrinsic ability. Thank you for the excellent advice, maze & quasar987. Considering special cases is invaluable for getting the gist of things, but I find it difficult to reconstruct (or even remember) the more general...

What are some methods of training one's mind to absorb and understand rigorous mathematical texts? I have been facing great difficulty as of late in studying fields like abstract algebra, complex analysis and calculus of variations. These are all fields where I am unable to formulate graphical...

Thanks for the responses. Dr. Courtney: I'm averse to flipping burgers for http://pictures.pichaus.com/95b70d92c70703496ea27d0c4ca3289315f1775f?AWSAccessKeyId=0K4RZZKHSB5N2XYJWF02&Expires=1207860000&Signature=a9%2BcuJEeSMway7k3BOxa5KokPxM%3D" . Getting hooked onto that job will eventually...

I'm a 3rd year Physics undergraduate student at the University of Toronto, and my academic career seems to have hit rock bottom. The grades from my past term were absolutely dismal and I have (consequently?) been rejected by various professors for summer work. Since I am effectively unemployed...

Thanks Hurkyl and gammamcc.

Is there a way to transform the limits of integration for a multivariable integral without appealing to geometrical manipulations? For example: \int_a^b \int_{y_1(x)}^{y_2(x)} \int_{z_1(x,y)}^{z_2(x,y)} f(x,y,z) \; dz \; dy\; dx \rightarrow \int_c^d \int_{y_3(z)}^{y_4(z)}...

Thanks everyone, I finally figured it out. Converting to spherical coordinates and using the law of cosines to represent the norm of the vector difference is needed.

My apologies. I had originally meant a spherical shell, from which the potential of an arbitrary spherically symmetric distribution can be computed. Gauss's theorem is certainly very useful, but the objective here is to compute the potential using the equation for \Phi only, without applying any...

Homework Statement I'm well aware of how to compute the gravitational [electric] potential \Phi due to a spherical mass [charge] distribution of radius R by using Newton's theorems for spherical shells. However, how does one find an analytic expression for \Phi without invoking these theorems...

That makes sense. I mistakenly thought there is a difference between \langle Q \rangle and \langle \hat{Q} \rangle, but that may have resulted from an abuse of notation. Thanks a lot, dextercioby.

Well yes, but that's simply the generalized form of the first equation I posted. So what you're saying is that they are the same? \left\langle \frac{\hat{p}}{m} \right\rangle = m^{-1}\int_{-\infty}^{\infty}\Psi^*\left(-i\hbar\frac{\partial}{\partial x}\right)\Psi \; dx?

I tried double application after I posted and got more elegant answers. Thanks dextercioby.

Homework Statement I know how to compute the expectation value of an observable. But how does one compute the expectation value of an observable's square? Homework Equations \langle Q \rangle = \int_{-\infty}^{\infty} \Psi^* \hat{Q} \Psi \; dx \langle Q^2 \rangle = \int_{-\infty}^{\infty}...