Recent content by bjogae

OK. Thank you. I figured I got something incorrectly. Does this mean that if William passed genes to Elizabeth he passed a complete chromosome? And that happened with 99.9999957% possibility? Just curious.

Actually, thinking of this in another way says that because of the law of large numbers about half of the coins will end up heads. Therefore we can calculate this as 25000\cdot0,5^{29}=4,66\cdot10^{-5}. Although if we think of how many ancestors one should have so nobody reproduces with someone...

This is not a homework question. It is actually kind of a biology question, but I'm dealing with the pure mathematics here. We came up with this reading "The selfish gene" by Richard Dawkins. He writes something like: "Elizabeth II is a direct decsendant William the conqueror. However it is...

one more try \psi(x,t)=\frac{1}{2\pi\hbar}\int dpe^{-i\sqrt{p^2c^2+m^2c^4}t/\\hbar}e^{ip x/\hbar} (\int \psi_0(x) e^{i p x/\hbar} dx) which shold be correct if k=\frac{p}{\hbar}

Of course. So the time dependent looks like i \hbar{\partial \over \partial t} \phi(p,\,t) = \hat H \phi(p,\,t) and for \hat H=\sqrt{p^2c^2+m^2c^4} it gives \phi(p,\,t) = \phi(p,\,0)e^{-i\sqrt{p^2c^2+m^2c^4}t/\hbar} which would lead to (by the previous reasoning)...

Thanks for the help.

Is this correct? It seems to be ok to me.

Homework Statement A charged harmonic oscillator is placed in an external electric field \epsilon i.e. its hamiltonian is H = \frac{p^2}{2m} + \frac{1}{2}m \omega ^2 x^2 - q \epsilon x Find the eigenvalues and eigenstates of energy Homework Equations The Attempt at a Solution...

So i get \phi_0(p)=\frac{1}{\sqrt{2\pi}} \int_k \psi_0(x) e^{i p x} ? Then i solve the time dependent as following: H\phi_0 = E \phi_0 \, where H=\sqrt{p^2c^2+m^2c^4} Is it so, that: \phi(p,\,t)= A(t) \phi_0(p) \ which leads to \Phi(p,\,t) = \phi_0(p) e^{-i{E t/\hbar}} \, and then...

Homework Statement The hamiltonian of a free relativistic particle moving along the x-axis is taken to be H=\sqrt{p^2c^2+m^2c^4} where p is the momentum operator. If the state of the wave function at time t=0 is described by the wave function \psi_0(x) what is the wave function at time t>0...

Homework Statement The group G acts transitively from the left on the set X. Let G_x be the little group of the element x \epsilon X. Show that the map i:G/G_x, i(gG_x)=gx is well defined and bijective. Homework Equations transitive action:for any two x, y in X there exists a g in G such...

Actually, no, i don't. I get that a cylinder is S1 × [0, 1], and I think I know how to find the atlas on a circle, I just feel so lost on how to apply it on a cylinder.

Homework Statement Find an atlas and coordinates for a torus T^2 = S^1 X S Homework Equations The Attempt at a Solution I know that an atlas on a manifold M is a collection of charts whose domains cover M, but i am not sure how to start this one mathematically.

Thanks, I think I got it right.

well I get stuck when I'm supposed to integrate a(x)^2*exp(i*2*p0*x/h). How do I do that?