Can you tell me how to learn and understand quantum dynamics

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Learning quantum dynamics requires mastering several prerequisite subjects. You need linear algebra for the mathematical framework, differential equations for solving the Schrödinger equation, classical mechanics especially Hamiltonian formalism, and basic quantum mechanics including wave functions and operators. The time-dependent Schrödinger equation is the fundamental equation of quantum dynamics. It describes how quantum states evolve over time under the influence of a Hamiltonian operator. The equation shows that the time derivative of a quantum state is proportional to the Hamiltonian acting on that state. Quantum mechanics can be formulated in three equivalent pictures. In the Schrödinger picture, quantum states evolve while operators remain fixed. In the Heisenberg picture, operators evolve while states stay constant. The interaction picture combines both approaches, useful for perturbation theory where both states and operators evolve. Time-dependent perturbation theory handles systems where the Hamiltonian has a small time-varying component. This approach calculates transition probabilities between quantum states, essential for understanding atom-light interactions and deriving Fermi's Golden Rule for transition rates. Learning quantum dynamics requires a structured approach. Start with simple systems to build intuition, focus on understanding the physical meaning behind equations, work through examples step by step, solve problems regularly, and connect different concepts. Remember that mastery comes through consistent practice and gradual building of understanding.