How Do You Calculate Transmission Amplitudes in Time-Dependent Tunneling?

Thread starter VictorTerra
Start date Mar 25, 2009
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Tunneling

In summary, time-dependent tunneling is a phenomenon in quantum mechanics where a particle can pass through a potential barrier despite having lower energy. This occurs due to the probabilistic nature of quantum mechanics and the wave-like behavior of particles. It happens when the particle's wave function extends beyond the barrier, allowing for a small but non-zero probability of passage. The probability of time-dependent tunneling is affected by the particle's energy, the barrier's height and width, and the duration of interaction between the two. It differs from time-independent tunneling, which refers to a constant barrier and does not consider the interaction duration. Time-dependent tunneling has practical applications in quantum computing, microscopy, and nanotechnology, as well as in understanding nuclear reactions, atoms

Mar 25, 2009

VictorTerra

Dear friends,how to calculate every transmission amplitude for each tunneling chanel in potential DeltaDirac(x- b*Sin(w*t))? Thanks for help...

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Mar 27, 2009

VictorTerra

ok... Can you help me with materials for time-dependent tunneling ?

FAQ: How Do You Calculate Transmission Amplitudes in Time-Dependent Tunneling?

What is time-dependent tunneling?

Time-dependent tunneling is a phenomenon in quantum mechanics where a particle can pass through a potential barrier even if its energy is lower than the barrier's height. This occurs due to the probabilistic nature of quantum mechanics and the wave-like behavior of particles.

How does time-dependent tunneling occur?

Time-dependent tunneling occurs when a particle is described by a wave function that extends beyond the potential barrier. This allows for a small but non-zero probability of the particle passing through the barrier, rather than being reflected or absorbed by it.

What factors affect the probability of time-dependent tunneling?

The probability of time-dependent tunneling is affected by the energy of the particle, the height and width of the potential barrier, and the duration of the interaction between the particle and the barrier. Higher energy particles and narrower barriers have a higher probability of tunneling.

How is time-dependent tunneling different from time-independent tunneling?

Time-dependent tunneling occurs when the potential barrier changes over time, while time-independent tunneling refers to a constant potential barrier. Time-dependent tunneling also takes into account the duration of the interaction between the particle and the barrier, which is not considered in time-independent tunneling.

What are some real-world applications of time-dependent tunneling?

Time-dependent tunneling has applications in various fields such as quantum computing, scanning tunneling microscopy, and nanotechnology. It is also crucial in understanding the behavior of particles in nuclear reactions and the stability of atoms and molecules.