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What is the logic for the Schr dinger equation - SS3 Physics Quantum Mechanics II Question

What is the logic for the Schrödinger equation?

 

The Schrödinger equation is a fundamental equation in quantum mechanics that describes the time evolution of a quantum mechanical state. The equation is a partial differential equation that describes how the wave function of a physical system changes over time. The wave function is a mathematical function that describes the probability amplitude of the system being in a particular state at a particular time.

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