I How is the Schrodinger equation related to the Heisenberg equation?

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The Schrödinger equation and the Heisenberg equation are two formulations of quantum mechanics that describe the same physical phenomena. In the Schrödinger picture, the states evolve over time while the operators remain constant, whereas in the Heisenberg picture, the operators evolve and the states are fixed. This distinction highlights the different approaches to understanding quantum systems, with both equations ultimately yielding equivalent predictions. The discussion emphasizes that these concepts are foundational in quantum mechanics and are covered in standard textbooks. Understanding their relationship is crucial for a deeper grasp of quantum theory.
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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Thread 'Antilinear Operators'

An antilinear operator ##\hat{A}## can be considered as, ##\hat{A}=\hat{L}\hat{K}##, where ##\hat{L}## is a linear operator and ##\hat{K} c=c^*## (##c## is a complex number). In the Eq. (26) of the text https://bohr.physics.berkeley.edu/classes/221/notes/timerev.pdf the equality ##(\langle \phi |\hat{A})|\psi \rangle=[ \langle \phi|(\hat{A}|\psi \rangle)]^*## is given but I think this equation is not correct within a minus sign. For example, in the Hilbert space of spin up and down, having...
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