Quantum Tunneling Calculator

Calculate Tunneling Probabilities and Transmission

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Rectangular Barrier Calculator

Calculate tunneling probability through a rectangular potential barrier.

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Alpha Decay Calculator

Calculate alpha particle tunneling probability and half-life.

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Understanding Quantum Tunneling

What is Quantum Tunneling?

Quantum tunneling is a quantum mechanical phenomenon where particles penetrate through potential barriers that they classically could not surmount. This effect has no classical analogue and is a direct consequence of wave-particle duality.

Key Concepts

Important aspects of tunneling:

  • Wave Function: Describes particle behavior
  • Barrier Penetration: Exponential decay inside barrier
  • Transmission Coefficient: Probability of tunneling
  • WKB Approximation: For varying potentials
  • Gamow Factor: For alpha decay

Applications

Quantum tunneling occurs in:

  • Nuclear fusion in stars
  • Alpha decay
  • Scanning tunneling microscopy
  • Quantum computing
  • Chemical reactions
  • Semiconductor devices

Historical Development

Key developments:

  • 1927: Wave mechanics explanation
  • 1928: Gamow explains alpha decay
  • 1957: Tunnel diode invention
  • 1981: Scanning tunneling microscope
  • Modern: Quantum technology applications

Essential Tunneling Formulas

Transmission Coefficient

T ≈ e^(-2κL)

Wave Vector

κ = √(2m(V₀-E))/ℏ

Gamow Factor

G = exp(-2π(αZ)√(2M/E))