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Quantum states evolve according to Schrödinger's equation from "summary" of The Principles of Quantum Mechanics by P. A. M. Dirac

The evolution of a quantum state is governed by Schrödinger's equation. This equation describes how the state of a quantum system changes over time. It provides a precise mathematical framework for understanding the dynamics of quantum systems. Schrödinger's equation is a differential equation that relates the time derivative of the quantum state to the Hamiltonian operator, which represents the total energy of the system. The equation is linear and deterministic, meaning that given an initial state, the future state of the system can be uniquely determined. The time evolution described by Schrödinger's equation is unitary, meaning that it preserves the normalization of the quantum state. This ensures that probabilities are conserved over time, allowing for a consistent interpretation of quantum mechanics. The Schrödinger equation is a cornerstone of quantum mechanics, providing a fundamental link between the dynamics of quantum systems and the underlying physical laws. It allows for the calculation of the evolution of a quantum state in a wide range of physical systems, from simple particles to complex molecules. By solving Schrödinger's equation, one can predict the behavior of quantum systems and make precise measurements of observables. The equation forms the basis for many important concepts in quantum mechanics, such as wavefunctions, eigenstates, and superposition.
  1. Schrödinger's equation plays a crucial role in our understanding of quantum physics, providing a powerful tool for describing the evolution of quantum states in a wide variety of physical systems.
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The Principles of Quantum Mechanics

P. A. M. Dirac

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