Tunneling Probability: Solving for Incident Angle $\theta$

In summary, the problem involves a particle of mass m incident on a planar barrier with a potential V(z)=\lambda\delta(x). The energy of the particle is E and the incident velocity makes an angle \theta with the z axis. The question is what is the probability of the particle penetrating the barrier. The solution for the case of normal incidence is known, but it is unclear how to incorporate the angle \theta into the problem. Further guidance or advice is needed for setting up the problem.
  • #1
keniwas
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Homework Statement


A particle of mass m is incident on a planar barrier which we represent by a potential . If the energy of the particle is E, and the incident velocity makes an angle with the z axis, what is the probability that the particle will penetrate the barrier?


The Attempt at a Solution


I can solve the problem for the case of normal incidence, as this is just the case of a delta potential barrier. However I have no idea how to include the incidence angle in the problem. This is where I am stuck, how/where does the angle come into the setup of the problem?
 
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  • #2
Anyone have any ideas on this? I just need some advice on how to setup the problem... I am lost on it =/
 

FAQ: Tunneling Probability: Solving for Incident Angle $\theta$

What is tunneling probability?

Tunneling probability is the likelihood of a particle passing through a potential barrier, such as an energy barrier, despite not having enough energy to overcome it. It is a concept in quantum mechanics that describes the behavior of particles at the subatomic level.

How is tunneling probability calculated?

Tunneling probability is calculated using the Schrödinger equation, which is a mathematical equation that describes the behavior of quantum particles. The equation takes into account the energy of the particle, the height and width of the potential barrier, and the angle of incidence.

What is the role of incident angle in tunneling probability?

The incident angle, denoted by $\theta$, is the angle at which the particle approaches the potential barrier. It plays a crucial role in determining the tunneling probability, as it affects the wavelength and energy of the particle. A higher incident angle can result in a lower tunneling probability, while a lower incident angle can result in a higher tunneling probability.

Can tunneling probability be greater than 1?

No, tunneling probability cannot be greater than 1. It is a probability value that ranges from 0 to 1, where 0 represents no probability of tunneling and 1 represents certain tunneling. It is a measure of the likelihood of a particle tunneling through a potential barrier, and therefore cannot exceed 1.

What factors can affect tunneling probability?

Several factors can affect tunneling probability, including the energy of the particle, the height and width of the potential barrier, and the incident angle. Other factors such as the mass and spin of the particle, as well as the shape of the potential barrier, can also impact tunneling probability.

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