1. Superposition
    • A quantum system can exist in a linear combination of states (e.g. Schrödinger’s cat).
    • Mathematically: |ψ⟩ = c₁|ψ₁⟩ + c₂|ψ₂⟩.
    (Schrödinger 1935)

  2. Wave–Particle Duality
    • Particles (electrons, photons) display both localized (“particle”) and delocalized (“wave”) behavior.
    • Illustrated by double‐slit experiments.
    (de Broglie 1924; Davisson & Germer 1927)

  3. Uncertainty Principle
    • Certain pairs of observables (e.g. position x and momentum p) cannot be simultaneously known with arbitrary precision:
    Δx·Δp ≥ ħ/2.
    (Heisenberg 1927)

  4. Measurement Problem
    • Upon measurement, a superposed state appears to “collapse” to a definite outcome.
    • Raises questions about the role of the observer and the ontology of the wavefunction.
    (von Neumann 1932; Wigner 1961)

  5. Entanglement and Non-locality
    • Two or more particles can share correlations that defy classical explanation.
    • Einstein–Podolsky–Rosen (EPR) argued this suggests “elements of reality” missing from quantum theory.
    • Bell’s theorem (1964) and subsequent experiments (Aspect 1982) show no local hidden‐variable theory can reproduce all quantum predictions.

Philosophical Interpretations
• Copenhagen (Bohr): Complementarity and observer-dependent phenomena.
• Many-Worlds (Everett 1957): Universal wavefunction never collapses; all outcomes occur in branching worlds.
• Bohmian Mechanics (Bohm 1952): Particles have definite positions guided by a “pilot wave.”
• Quantum Bayesianism (QBism): Wavefunction reflects an agent’s personal degrees of belief.

Key References
– Heisenberg, W. “Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik” (1927)
– Schrödinger, E. “Die gegenwärtige Situation in der Quantenmechanik” (1935)
– Bell, J. S. “On the Einstein Podolsky Rosen Paradox” (1964)

  1. Superposition
    • Stern–Gerlach with spin-½ particles: before measurement, the beam is in |↑⟩+|↓⟩ and only “chooses” one axis on detection.
    • Schrödinger’s cat: a radioactive decay both “decayed” and “undecayed” until an observer opens the box. (Schrödinger 1935)

  2. Wave–Particle Duality
    • Electron double‐slit: individual electrons form an interference pattern over time, yet each hits the screen at a single point. (Davisson & Germer 1927)
    • Single‐photon Mach–Zehnder interferometer: behaves like a wave (interference) unless a detector is placed in one arm.

  3. Uncertainty Principle
    • Electron diffraction by a narrow slit: narrower slit (Δx↓) ⇒ wider spread on the screen (Δp↑).
    • Homodyne detection in quantum optics: precise phase (quadrature) measurement increases photon‐number uncertainty.

  4. Measurement Problem
    • Wigner’s friend: an observer inside a sealed lab sees a definite outcome, while an outside “Wigner” assigns a superposed state to the entire lab. (Wigner 1961)
    • Quantum Zeno effect: rapid repeated measurements “freeze” a system’s evolution, highlighting the role of measurement.

  5. Entanglement and Non‐locality
    • Bell test experiments (Aspect 1982): polarization‐entangled photons violate Bell inequalities, ruling out local hidden variables.
    • Quantum teleportation: uses an entangled pair and classical communication to transfer an unknown quantum state. (Bennett et al. 1993)

Philosophical Interpretation Examples
• Copenhagen: Complementarity in Bohr’s hydrogen‐spectral‐line experiments—wave and particle descriptions are mutually exclusive but jointly exhaustive.
• Many-Worlds: Quantum computing’s parallelism is often portrayed as computation across branching worlds. (Everett 1957)
• Bohmian Mechanics: “Trajectories” reconstructed in weak‐measurement double‐slit setups mimic pilot‐wave predictions. (Kocsis et al. 2011)
• QBism: Photon‐counting statistics in quantum tomography are viewed as an agent’s personal probability assignments rather than objective wavefunction collapse.

Definition
• Intrinsic angular momentum: a quantum degree of freedom with magnitude √(s(s+1))ħ (here s=½), so each measurement along any axis yields ±ħ/2.
• Fundamentally two-level (“qubit-like”) system, not arising from literal spinning.

Experimental Signature
• Stern–Gerlach (1922): silver atoms deflected into two discrete spots, revealing ±½ħ projections. (Stern & Gerlach 1922)
• Electron spin resonance (ESR): transitions between spin-up and spin-down in a magnetic field produce characteristic absorption frequencies.

Physical Consequences
• Magnetic moment μ = g(eħ/2m): underpins electron paramagnetism, NMR/MRI imaging, and spintronics devices.
• Pauli exclusion principle: no two electrons (spin-½ fermions) occupy the same quantum state ⇒ atomic shell structure and chemistry. (Pauli 1925)
• Fine and hyperfine spectral splitting in atoms: electron spin coupling to orbital motion and nuclear spin.

Technological Applications
• Quantum computing: electron or nuclear spins serve as qubits with long coherence times.
• Spintronics: manipulation of spin currents for nonvolatile memory (MRAM) and logic.

References
• Stern, W. & Gerlach, O. “Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld” (1922)
• Pauli, W. “Über den Zusammenhang des Abschlusses der Elektronengruppen im Atom mit der Komplexstruktur der Spektren” (1925)

Back to Graph