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

[Show all videos]
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

[Show all illustrations]
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
Energiequantisierung im quadratischen Potential
Energy quantization - quadratic potential energy function
Wellenfunktion im verbotenen Bereich
Wave function in the classically forbidden / allowed region
Klassisch verbotener/erlaubter Bereich
Classically forbidden / allowed region
Betragsquadrat (Beispiel) - Normierungsbedingung ergibt Wahrscheinlichkeit 1
Squared magnitude - Normalization condition - Integration over the entire space
Ebene Welle im Zeigerdiagramm
Plane wave in a complex plane
Eine eindimensionale ebene Welle, die sich nach rechts ausbreitet.
Harmonic plane wave (1d) - Propagation
De-Broglie-Wellenlänge
De-Broglie wavelength
Betragsquadrat einer Wellenfunktion (Beispiel)
Squared magnitude of a wave function (example)
Fermi distribution graph at finite temperature
Fermi distribution graph at finite temperature