In square antiprism the squares to not overlay each other, they are staggered 45 degrees. But thank you for showing me antiprisms, very neat structures to try to do molecular symmetry on.
A dodecahedron has too many coordinates from what I see but also an interesting structure.
The...
Main question: What is the name of the 8 coordinate complex pointgroup? Or does it even exist?
I've been exposed to octahedrons and icosohedrons, however, the 8 coordinate high symmetry complexes appear to have been skipped. I'm aware that these complexes would be rare but I think that...
Thank you both for the contrasting notations. Is there anything I can do to return the help?
=\sum_n\sum_m c_n^*c_m a_m\langle\psi_n,\psi_m\rangle=\sum_n|c_n|^2 a_n
Very elegant. The absolute value of the complex conjugates is a clever touch. I've not used complex number enough to...
What do you mean by substitute the 'entire' \Psi and \Psi*, simply that I didn't denote the first wavefunction with asterisks fully? Or do you mean literally put in c21, c2, c3, etc.?
Anyways here was an attempt at this.
\int(c^*_n\Psi^*_n\hat A)(\hat Ac_n\Psi_n)
c^*_n...
The \Psiis linear combination of n orthonormal eigenfunctions of the linear operator, A(hat).
What effect does a normalized function vs a 'orthonormal' function have on the 'expectation value'? Sorry I'm being thrown into this terminology very rudely. Any help is greatly appreciated.
\int c*n\Psin \left| A(hat) \right| cn \Psin
I'm having trouble putting subscript into the LaTex format, is there a way to do this without breaking pup the tex formatting?
I'm trying to substitute the psi function into the expectation value. I do not understand how to use the asterisk in this case. Especially if the constants in the function are complex... I'm trying to understand the concept and am unsure what to ask.
I've never seen an expectation value taken and would greatly appreciate seeing a step by step of how it is done. Feel free to use any wavefunction, this is the one I've been trying to do:
In the case of \Psi=c1\Psi1 + c2\Psi2 + ... + cn\Psin
And the operator A(hat) => A(hat)\Psi1 =...
In the case of \Psi=c1\Psi1 + c2\Psi2 + ... + cn\Psin
And the operator A(hat) => A(hat)\Psi1 = a1\Psi1; A(hat)\Psi2 = a2\Psi2; A(hat)\Psin = an\Psin
Calculate: \left\langle\Psi\left|A(hat)\right|\right\Psi\rangle
So that's where that comes from ;) I'm having trouble identifying all the equations from very similar ones. You seem to have a keen grasp of QM, where did you learn from? Some kind of organization in this maelstrom of QM ideas and variables would be nice...
I've seen similar ideas but never...
When linear operators A and B act on a function ψ(x), they don't always commute. A clear example is when operator B multiplies by x, while operator A takes the derivative with respect to x. Then
which in operator language means that
To get the last equation they divided through by ψ...
Thanks for the clarification. It's a measurement of the extent to which they do NOT commute, correct? I do not see where a non-zero commutator would be useful though.
Does LzLx = LxLz ? I want to know if the relations hold true for both of them or if I have to add a negative sign (or something of that nature). Don't angular momentums commute?