How is the Schrodinger equation related to the Heisenberg equation?

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SUMMARY

The Schrödinger equation and the Heisenberg equation are two fundamental formulations of quantum mechanics that describe the evolution of quantum systems. In the Schrödinger picture, the states evolve over time while operators remain constant, whereas in the Heisenberg picture, operators evolve and states remain fixed. Both formulations are equivalent and can be found in standard quantum mechanics textbooks such as those by Sakurai and Shankar. Understanding these distinctions is crucial for grasping the principles of quantum mechanics.

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  • Quantum Mechanics fundamentals
  • Schrödinger equation
  • Heisenberg equation
  • Quantum state evolution
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  • Study the equivalence of the Schrödinger and Heisenberg formulations in detail
  • Explore the implications of state and operator evolution in quantum mechanics
  • Review quantum mechanics textbooks, specifically Sakurai and Shankar
  • Investigate the mathematical foundations of quantum mechanics, including linear operators
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Students and professionals in physics, particularly those specializing in quantum mechanics, as well as educators seeking to deepen their understanding of quantum theory formulations.

Thamyres MARTINS
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How is the Schrondinger equation related to the Heisenberg equation?
 
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Thamyres MARTINS said:
How is the Schrondinger equation related to the Heisenberg equation?
You marked this thread as "A" level. That indicates that you have a graduate level background in the subject matter. If you do have such a background, you should already know the answer to this question.

What is your actual background in QM?
 
And in the meantime, the thread level has been set to "I", perhaps more appropriate for the question.
 
Should be treated in all QM textbooks I guess (like Sakurai, Shankar). In the Schrödinger picture, the states evolove and operators do not, in the Heisenberg picture it is the other way around. Thus, the Schrödinger equation deals with the time evolution of states, and the Heisenberg equation deals with the time evolution of operators.
 
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