Hamiltonian Problem (Quantum Mechanics)

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SUMMARY

The discussion centers on calculating the expectation value of a 3x3 matrix operator in quantum mechanics, given a state |ψ>. The user has successfully determined the eigenvalues but struggles with applying the generalized formula for expectation values, particularly regarding the inclusion of the hermitian conjugate. The conversation emphasizes the importance of providing sufficient context and attempts when seeking help in complex topics like quantum mechanics.

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  • Understanding of quantum mechanics principles, specifically eigenvalues and eigenstates.
  • Familiarity with matrix operators in quantum systems.
  • Knowledge of expectation values and their calculation in quantum mechanics.
  • Experience with hermitian operators and their properties.
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  • Study the calculation of expectation values in quantum mechanics using matrix operators.
  • Learn about hermitian conjugates and their role in quantum mechanics.
  • Explore examples of expectation value calculations for 3x3 matrices.
  • Review the properties of eigenvalues and eigenstates in quantum systems.
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Students and professionals in quantum mechanics, physicists working with matrix operators, and anyone seeking to deepen their understanding of expectation values in quantum systems.

Just_some_guy
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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
 
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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
 

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