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Thamyres MARTINS
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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.Thamyres MARTINS said:How is the Schrondinger equation related to the Heisenberg equation?
The Schrödinger equation is a fundamental equation in quantum mechanics that describes how the quantum state of a physical system changes over time. It is a partial differential equation that governs the wave function of a system, encapsulating its dynamics and evolution.
The Heisenberg equation, also known as the Heisenberg equation of motion, describes the time evolution of operators in quantum mechanics. It is derived from the Heisenberg picture, where the operators evolve with time while the state vectors remain constant.
The Schrödinger and Heisenberg equations are two different formulations of quantum mechanics. They are mathematically equivalent and provide the same physical predictions. The Schrödinger equation focuses on the wave function's time evolution, while the Heisenberg equation focuses on the time evolution of operators. Both approaches are linked through unitary transformations.
Yes, the Heisenberg equation can be derived from the Schrödinger equation. By applying the time-dependent Schrödinger equation to the expectation value of an operator and using the commutation relations, one can obtain the Heisenberg equation of motion, which describes how operators evolve over time.
Neither the Schrödinger equation nor the Heisenberg equation is more fundamental than the other; they are two representations of the same underlying quantum mechanics. The choice between them depends on the context and the problem being solved. Both formulations are equally valid and provide the same information about a quantum system.