Homework Statement
Find the other sp hybrid orbital given \Psi_{sp1} = 3\Psi_{2s} + 4\Psi_{2pz} using the orthonormal relationships.
I do not know how to start the problem. if someone could help get me pointed in the right direction or help me through it I would greatly appreciate it : )
how did you get that? it was given in the problem that the true initial value is
0.125h^{2}/m_{e}a^{2}
or .0199h^{2}/m_{e}a^{2}
did you plug the k value into E_{min}=(h^{2}/m_{e}a^{2})(4k^{2}+k)/(2k-1)
is there anyway you could work through the problem and double check my work? I've worked through it twice now and still haven't gotten an answer that looks right
ok. sorry, dumb moment.
so I solved for k=-.11237 and k=1.11237.
then I plugged the positive k value into E and got 3.133(h^{2}/m_{e}a^{2}) or 19.68(h^{2}/m_{e}a^{2}) which isn't even in the ballpark of the true value.
Okay, but if the value of k is 0, then that doesn't go with the problem. In the problem it states that there will be a positive and negative value for the parameter and it asks why the positive number is better. And if k is 0 then the approximation won't work when you plug back into E_{min}
the derivative doesn't seem to be solveable because there's no way to move anything over to the other side. and I know that I'll get multiple values of k when I solve.
I'm having problems deriving and solving for k. When I take the derivative, I get
dE/dk=(h/(m_{e}a^{2})(8k^{2}-8k-1)/(1-2k)^{2}=0
and I'm having problems solving for it. am I doing something wrong?
Homework Statement
use the variational method to approximate the ground state energy of the particle in a one-dimentional box using the normalized trial wavefunction ∅(x)=Nx^{k}(a-x)^{k} where k is the parameter. Demonstrate why we choose the positive number rather than the negative...
Ok I've set up the integral like this:\ointsin^{3}\theta*dv with the bounds being 0 to 2pi for phi, and 0 to pi for theta. I left out r because it will make the integral go to infinity, but I'm still getting a pi in the answer. when I left out the phi part of the integral I got 4/3. what am I...
I know it needs to be switched to polar coordinates and your equation you posted is correct. I know that it is normalizable (1=int(psi^2dv) over all space, i just need a confirmation of the correct set up of the integral and the bounds. I've tried it several different ways with different bounds...