Introduction to Quantum Mechanics - Prüfungsnummer 9958442

Why Quantum Mechanics? Limits of Classical Physics

• Why was classical physics considered complete around 1900?
• What went wrong?
• Why do engineers need quantum mechanics?

Waves, Particles, and the Double-Slit Experiment

• Nature does not behave like particles or waves.

Probability, Measurement, and the Uncertainty Principle

• Measurement as an active process
• Probability amplitudes vs. probabilities
• Position–momentum uncertainty

Mathematical Tools I: Complex Numbers, Vectors, Probabilities

• Complex numbers as physical tools
• Absolute value, phase
• Vectors and superposition
• Probability amplitudes
• Normalization
  Engineering perspective
• Relation to signal processing
• Relation to linear systems

Mathematical Tools II: States, Superposition, and Linear Algebra

• Concept of a “state”
• Basis states
• Superposition principle
• Measurement outcomes as projections
• Simple two-state systems

Time Evolution and Energy Quantization

• Time dependence of quantum states
• Stationary states
• Energy as an eigenvalue
• Why energy becomes quantized
• Simple bound systems

The Schrödinger Equation: Meaning, Not Derivation

• Wave function and its interpretation
• Schrödinger equation as a rule, not a proof
• Physical meaning of terms
• Alternative descriptions

Tunneling and Non-Classical Effects

• Potential barriers
• Quantum tunneling
• Why classical physics forbids it
• Real-world implications
  Applications
  • Scanning tunneling microscope
  • Semiconductor devices
  • Nuclear fusion (basic idea)

Spin and Quantum Information

• Spin as intrinsic quantum property
• Stern–Gerlach experiment
• Two-level systems
• Measurement outcomes
  Engineering relevance
  • MRI
  • Quantum bits (conceptual only)

From Atoms to Solids: Quantum Origin of Materials

• Atomic energy levels
• Electron shells
• Band structure (qualitative)
• Conductors, insulators, semiconductors

Technological Successes of Quantum Mechanics

• Transistors
• Lasers
• LEDs
• Solar cells
• Modern electronics
• Medical imaging

Outlook: Quantum Mechanics Today and Tomorrow

• What quantum mechanics does not explain
• Interpretation debates (brief, careful)
• Quantum technology:
• Sensors
• Communication
• Computing (realistic view)

Dozent/in: Hr. Dr. Hartmann
Stand: 05.03.2026, 16:27