Learn the time (in)dependent Schrodinger equation and what the wave function is.
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</p><p>In this quantum mechanics lecture you will learn the Schrodinger equation (1d and 3d, time-independent and time-dependent) within 45 minutes. In the beginning, you will learn the difference between classical mechanics and quantum mechanics and some applications of the Schrodinger equation.
</p><p>Then we derive the one-dimensional time-independent Schrodinger equation (SEQ) and uncover the basic principles of the Schrodinger equation - energy conservation and wave-particle duality. Afterwards, you will learn its statistical Interpretation (Copenhagen Interpretation) and the associated squared magnitude of the wave function. After that, we study the general behavior of the wave function in the classically allowed and forbidden regions and the resulting energy quantization. We then generalize the one-dimensional Schrodinger equation to the three-dimensional version and encounter the Laplace and Hamilton operator. With the latter we formulate the Schrodinger equation as an eigenvalue equation.
</p><p>Then we move on to the time-dependent Schrodinger equation and try to motivate ("derive") it with a little magic. And finally we apply the powerful separation of variables to the time-dependent Schrodinger equation to simplify the solving of the differential equation. As a result, we get stationary states and the stationary Schrodinger equation, which is much easier to solve than the time-dependent version.
</p><p>Video content:
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<hr><p>00:00 What is a partial second-order DEQ? 
00:58 Classical Mechanics vs. Quantum Mechanics
04:27 Applications
05:14 Derivation of the time-independent Schrodinger equation (1d)
17:14 Squared magnitude, probability and normalization
25:26 Wave function in classically allowed and forbidden regions
35:34 Time-independent Schrodinger equation (3d) and Hamilton operator
38:18 Time-dependent Schrodinger equation (1d and 3d)
41:18 Separation of variables and stationary states
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</p><p>About the channel:
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<hr><p>Here you will find high quality free physics videos for beginners and advanced students.
</p><p>About the author:
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<hr><p>I am Alexander Fufaev, I am a physicist from Germany. I run the physics website universaldenker.org
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