SCHRÖDINGER'S EQUATION (Derivation) - Plausibility Argument & Time-Independent SE Derivation

What is the Schrodinger Equation? Can we Derive it? What is it's role in Quantum mechanics?
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The Schrödinger Equation is a fundamental equation in quantum mechanics that describes how the quantum state of a physical system changes over time. Ψ(r,t) is the wave function of the system, which provides the probability amplitude for the position and state of a particle at a given time. The equation is key to predicting how quantum systems evolve over time and underpins much of modern physics.
The time-independent Schrödinger Equation is a key concept in quantum mechanics, used for analyzing situations where the energy in the system does not change with time. This form of the equation focuses on stationary states - scenarios where the probability of finding particles in certain positions remains constant over time. It's particularly useful for studying systems with unchanging potential energy, like atoms and molecules in stable conditions.
00:00 Introduction
02:33 Schrödinger Equation
09:28 Plausibility Argument for Schrödinger Equation
37:50 Time-Independent Schrödinger Equation Derivation
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