2.2 Quantum tunneling and barrier penetration

Quantum tunneling is a mind-bending concept where particles can pass through barriers they shouldn't be able to. It's all thanks to the wave-like nature of matter at the quantum level. This phenomenon challenges our everyday understanding of physics.

Tunneling has real-world applications in electronics, microscopy, and nuclear physics. It's the secret sauce behind tunnel diodes, scanning tunneling microscopes, and even radioactive decay. Understanding tunneling is key to grasping quantum mechanics.

Quantum Tunneling Fundamentals

Understanding Quantum Tunneling

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• Quantum tunneling occurs when a particle passes through a potential barrier that it classically could not surmount
• Particles exhibit wave-particle duality, allowing them to penetrate barriers with a certain probability (tunneling probability)
• The tunneling probability depends on the particle's energy and the barrier's height and width
• Quantum tunneling is a fundamental consequence of the wave nature of matter and the Heisenberg uncertainty principle

Potential Barriers and Transmission Coefficients

• A potential barrier is a region where the potential energy of a particle is higher than its kinetic energy
• The transmission coefficient ($T$) quantifies the probability of a particle tunneling through a potential barrier
• $T$ is calculated using the particle's energy, the barrier's height, and the barrier's width
• The transmission coefficient decreases exponentially with increasing barrier width and height

Quantum Tunneling Applications

Tunnel Diodes in Electronics

• A tunnel diode is a semiconductor device that utilizes quantum tunneling for its operation
• Electrons can tunnel through the p-n junction barrier, resulting in a negative resistance region in the I-V characteristics
• Tunnel diodes find applications in high-speed switching, oscillators, and amplifiers due to their fast response times
• Example applications include high-frequency oscillators and low-noise amplifiers in wireless communication systems

Scanning Tunneling Microscopy for Surface Analysis

• Scanning tunneling microscope (STM) is a powerful tool for imaging and manipulating individual atoms on surfaces
• STM relies on the quantum tunneling of electrons between a sharp conducting tip and a sample surface
• The tunneling current depends on the tip-sample distance, allowing the STM to map the surface topography with atomic resolution
• STM has revolutionized surface science, enabling the study of atomic-scale structures, defects, and electronic properties (graphene, carbon nanotubes)

Quantum Tunneling in Nuclear Physics

• Alpha decay is a radioactive decay process in which an atomic nucleus emits an alpha particle (helium nucleus)
• The alpha particle is initially confined within the nucleus by a potential barrier but can escape via quantum tunneling
• The tunneling probability determines the half-life of the radioactive isotope undergoing alpha decay
• Alpha decay is a prime example of quantum tunneling in nuclear physics and is used in radiometric dating (uranium-lead dating)