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

XIn summary, the Feynman lectures briefly mention the Hamiltonian matrix constructed in Chapter 8 and its relation to the Heisenberg matrix picture. However, the lectures do not go into detail about the Heisenberg representation, which is a formulation of matrix mechanics in an arbitrary basis where the operators incorporate a time dependency and the state vectors are time-independent. This is in contrast to the Schrodinger representation where the operators are constant and the states evolve in time.
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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
 

1. What is the Heisenberg matrix picture mentioned in Feynman Lecture Vol III Ch. 8?

The Heisenberg matrix picture is a mathematical framework used to describe the behavior of quantum systems. It is based on the Heisenberg uncertainty principle, which states that the more precisely we know the position of a particle, the less we know about its momentum, and vice versa.

2. How does the Heisenberg matrix picture differ from the Schrödinger picture?

In the Schrödinger picture, the states of a quantum system are represented by wavefunctions that evolve in time. In the Heisenberg matrix picture, the states are represented by operators that do not change with time, and the observables of the system are represented by matrices that evolve in time.

3. What is the significance of the Heisenberg matrix picture in quantum mechanics?

The Heisenberg matrix picture provides a mathematical framework for calculating the dynamics of quantum systems and making predictions about their behavior. It also helps to reconcile the classical notion of particles with the strange behaviors observed in the quantum world.

4. Can the Heisenberg matrix picture be applied to all quantum systems?

Yes, the Heisenberg matrix picture can be applied to all quantum systems, regardless of their complexity. It is a fundamental concept in quantum mechanics and is used extensively in calculations and theoretical models.

5. How does the Heisenberg matrix picture relate to the uncertainty principle?

The Heisenberg matrix picture is based on the Heisenberg uncertainty principle, which is a fundamental principle of quantum mechanics. This principle states that the more precisely we know the position of a particle, the less we know about its momentum, and vice versa. The Heisenberg matrix picture provides a mathematical formalism for understanding and calculating the uncertainties in a quantum system.

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