Quantum mechanics

Lesson Level 3

Schrödinger Equation and The Wave Function

Betragsquadrat einer Wellenfunktion (Beispiel)

In this lesson you will learn about the Schrödinger equation, where it comes from and what you can do with it.

Videos

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Video Level 3

Schrodinger Equation explained extensively in 50 minutes!

Schrodinger Equation

In this quantum mechanics lecture you will learn the Schrödinger equation (1d and 3d, time-independent and time-dependent) within 45 minutes.

Content of the video
  1. [00:10] What is a partial second-order DEQ?
  2. [01:08] Classical Mechanics vs. Quantum Mechanics
  3. [04:38] Applications
  4. [05:24] Derivation of the time-independent Schrödinger equation (1d)
  5. [17:24] Squared magnitude, probability and normalization
  6. [25:37] Wave function in classically allowed and forbidden regions
  7. [35:44] Time-independent Schrödinger equation (3d) and Hamilton operator
  8. [38:29] Time-dependent Schrödinger equation (1d and 3d)
  9. [41:29] Separation of variables and stationary states

Illustrations

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De-Broglie-Bohm-Theorie: Teilchenbahnen beim Doppelspalt
De-Broglie-Bohm theory: Particle trajectories at the double slit
Fermi, Bose and Boltzmann distribution - Graphs
Fermi, Bose and Boltzmann distribution graphs
Bose distribution graph
Bose distribution graph
Energy levels - infinite potential well (1d)
Energy levels - infinite square potential well (1d)
Wave functions - Infinite square potential well (1d)
Infinite square potential well (1d) - Wave functions
Angular momentum - space-quantization
Angular momentum - space-quantization
Quantization of energy in the quadratic potential
Energy quantization - quadratic potential energy function
Wave function in the forbidden region
Wave function in the classically forbidden / allowed region
Classic forbidden/allowed regions
Classically forbidden / allowed region
Absolute square (example) - normalization condition results in probability 1
Squared magnitude - Normalization condition - Integration over the entire space
Absolute square of a wave function (example)
Squared magnitude of a wave function (example)
Plane wave in complex plane
Plane wave in a complex plane
A one-dimensional plane wave propagating to the right
Harmonic plane wave (1d) - Propagation
Fermi distribution graph at finite temperature
Fermi distribution graph at finite temperature
De Broglie wavelength
De-Broglie wavelength