Feynman Lecture Vol III Ch. 8 Question -- Heisenberg matrix picture

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SUMMARY

The Hamiltonian matrix discussed in Chapter 8 of the Feynman Lectures serves as an introduction to the matrix representation of Hamiltonians but does not delve into the Heisenberg matrix picture in detail. The Heisenberg picture is characterized by time-dependent operators while keeping state vectors time-independent, contrasting with the Schrödinger representation where operators remain constant and states evolve over time. The discussion clarifies that the Hamiltonian matrix is not synonymous with the Heisenberg representation.

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kq6up
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Is the Hamiltonian matrix that is constructed in Ch 8 of the Feynman lectures the Heisenberg matrix picture, or is it something else? I am just curious.

Thanks,
Chris Maness
 
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kq6up said:
Is the Hamiltonian matrix that is constructed in Ch 8 of the Feynman lectures the Heisenberg matrix picture, or is it something else? I am just curious.

Thanks,
Chris Maness
The Heisenberg picture or representation is a formulation of in which the operators and others incorporate a dependency on time, but the state vectors are time-independent, an arbitrary fixed basis rigidly underlying the theory.

It stands in contrast to the schrodinger representation in which the operators are constant, instead, and the states evolve in time. The Heisenberg picture is the formulation of matrix mechanics in an arbitrary basis, in which the Hamiltonian is not necessarily diagonal.

the reference in ch-8 of Feynman lectures is just an intro to matrix representation of Hamiltonian and does not deal in detail the Heisenberg representation.
 
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Thank you. Perfect answer.

Regards,
Chris KQ6UP
 

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