Hamiltonian Problem (Quantum Mechanics)

Just_some_guy
Messages
16
Reaction score
0
Hi everyoneI have been give a matrix operator and asked to find the eigen values, I have done so and then I was given a state |ψ> of some particle.

The part I'm struggling with is it then asks for <H>, the expectation value of the matrix operator. It's a 3x3 matrix also.

I've tried using the generalised formula for expectation value but I've only ever used it for simple probability densities

I've looked all over the internet to find an example even a little close and had no joy whatsoever :(

Any ideas or guidance would be much appreciated :)Regards
 
Physics news on Phys.org
Hi
You should give us enough information and also show some attempt.
 
ImageUploadedByPhysics Forums1420575853.597092.jpg
Above is the only thing I'm unsure about! Does the hermitian conjugate of the include the constant or not? Other than that I think I've solved the problem?
Thanks
 
Hi, I had an exam and I completely messed up a problem. Especially one part which was necessary for the rest of the problem. Basically, I have a wormhole metric: $$(ds)^2 = -(dt)^2 + (dr)^2 + (r^2 + b^2)( (d\theta)^2 + sin^2 \theta (d\phi)^2 )$$ Where ##b=1## with an orbit only in the equatorial plane. We also know from the question that the orbit must satisfy this relationship: $$\varepsilon = \frac{1}{2} (\frac{dr}{d\tau})^2 + V_{eff}(r)$$ Ultimately, I was tasked to find the initial...
The value of H equals ## 10^{3}## in natural units, According to : https://en.wikipedia.org/wiki/Natural_units, ## t \sim 10^{-21} sec = 10^{21} Hz ##, and since ## \text{GeV} \sim 10^{24} \text{Hz } ##, ## GeV \sim 10^{24} \times 10^{-21} = 10^3 ## in natural units. So is this conversion correct? Also in the above formula, can I convert H to that natural units , since it’s a constant, while keeping k in Hz ?
Back
Top