Recent content by PhyPsy

The recent WMAP data has narrowed the range of possible curvatures of the universe, but unfortunately, it still leaves open the possibilities of a universe with positive or negative curvature. I suppose you could say it makes the possibility of a flat universe more likely, but if the universe...

I've read about theories that state not only did matter as we understand it not exist before 13.7 billion years ago, but spacetime itself did not exist before then. I understand that GR posits a singularity at that time in history, but does this mean spacetime itself did not exist before then? I...

I've given this a lot of thought the last couple days. I look at the Hubble equation v=H_0 d, and I don't see how this necessitates everything existing in a single point at some time in the past. Certainly, everything was really close together 13.7 billion years ago, but not in an infinitely...

OK, so then for systems that are not a superposition, how do you know whether to use a or b? I understand that for atoms where both electrons have the same value for n, the antisymmetric space function is equal to 0, so you have to pick a, but what about atoms where the electrons have different...

For the first excited state of the atom, one electron is in the lowest energy level n=1, and the other is in the level n=2. According to your statement, there should be a superposition, but the answer only contains a b (from my initial post) term and no a term.

For a two-electron atom, this book says that the overall wave function is either a) the symmetric space function times the antisymmetric spin function or b) the antisymmetric space function times the symmetric spin function. However, in another problem which involves two fermions in a harmonic...

Your tip led me to realize that it would be simpler to think of it as a rotation applied to \mid j,m \rangle. Then, I can use the Wigner D-matrix to simplify the expression: R(\alpha , \beta , \gamma) \mid j,m \rangle =\sum _{m'=-j} ^j D _{m'm} ^{(j)} (\alpha , \beta , \gamma) \mid j,m' \rangle...

Homework Statement Prove that e^{-i \pi J_x} \mid j,m \rangle =e^{-i \pi j} \mid j,-m \rangle Homework Equations J_x \mid j,m \rangle =\frac{\hbar}{2} [\sqrt{(j-m)(j+m+1)} \mid j,m+1 \rangle + \sqrt{(j+m)(j-m+1)} \mid j,m-1 \rangle] The Attempt at a Solution Expanding e^{-i \pi J_x}...

Actually, \psi (x) is the Fourier transform of \phi (k), or at least it is supposed to be... \psi (x)= \frac{1}{\sqrt{2 \pi}} \int ^\infty _{-\infty} \phi(k) e^{ikx} dk =\frac{\sqrt{3}}{2 \sqrt{\pi a^3}} [\int ^0 _{-a} (a+k)e^{ikx} dk + \int ^a _0 (a-k)e^{ikx} dk] =\frac{\sqrt{3}}{2...

\langle A\rangle=0 for both functions, so (\Delta a)^2= \int ^\infty _{-\infty}a^2 f(a) da (\Delta k)^2= \int ^\infty _{-\infty} k^2 |\phi(k)|^2 dk = \frac{3}{2a^3} [\int ^0 _{-a} k^2 (a+k)^2 dk + \int ^a _0 k^2 (a-k)^2 dk] =\frac{3}{2a^3} [(\frac{1}{3} a^2 k^3 + \frac{1}{2} a k^4 + \frac{1}{5}...

Uncertainty values for non-Gaussian wave packet functions Homework Statement \phi(k)= \left\{ \begin{array}{cc} \sqrt{\frac{3}{2a^3}}(a-|k|), & |k| \leq a \\ 0, & |k|>a \end{array} \right. \psi(x)= \frac{4}{x^2}sin^2 (\frac{ax}{2}) Calculate the uncertainties \Delta x and \Delta p and check...

How do you come up with this approximation? [1+H(t-t_0)- \frac{1}{2}qH^2(t- t_0)^2]^{-1}\approx1+ H(t_0-t)+ \frac{1}{2}qH^2(t-t_0)^2+ H^2(t-t_0)^2 Is there a rule that leads to this approximation?

Bah, you're right, since \rho is a function of r, I can't use it as a constant. My bad. Ha ha, I'm actually in IT myself, though I am not a hardcore programmer; I do some here and there. Physics is a very interesting subject to me, but a career in it, on the other hand, doesn't appeal to me...

Doing the math in my head, the constant would have to be \ln(\rho-m). The constant from integration of the left side of the equation allows for the rho term. I risk leaving the topic of this forum by asking this, but every book and article I have seen uses the specific transformation...

Homework Statement \frac{dr}{\sqrt{r^2- 2mr}}= \frac{d\rho}{\rho} Solve for r. Homework Equations The Attempt at a Solution For those familiar with GR, this is an attempt to come up with the isotropic form of the Schwarzschild solution to the field equations, but I'm having trouble...