Tunneling Probability: Solving for Incident Angle $\theta$

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SUMMARY

The discussion focuses on calculating the tunneling probability of a particle with mass m incident on a planar barrier represented by a potential V(z) = λδ(x). The challenge arises when incorporating the incident angle θ with respect to the z-axis into the solution. While the normal incidence case is solvable using the delta potential barrier model, the participants seek guidance on how to adjust the setup to account for the angle θ, which is critical for determining the tunneling probability accurately.

PREREQUISITES
  • Quantum mechanics fundamentals, specifically wave-particle duality.
  • Understanding of potential barriers and tunneling phenomena.
  • Familiarity with delta function potentials in quantum mechanics.
  • Basic knowledge of angular momentum and its implications in quantum systems.
NEXT STEPS
  • Study the mathematical formulation of tunneling probabilities in quantum mechanics.
  • Explore the impact of incident angles on wave functions in quantum mechanics.
  • Learn about the Schrödinger equation solutions for delta potentials.
  • Investigate the role of angular momentum in quantum tunneling scenarios.
USEFUL FOR

Students and researchers in quantum mechanics, particularly those studying tunneling phenomena and potential barriers. This discussion is especially beneficial for those tackling problems involving non-normal incidence angles in quantum systems.

keniwas
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Homework Statement


A particle of mass m is incident on a planar barrier which we represent by a potential [tex]V(z)=\lambda\delta(x)[/tex]. If the energy of the particle is E, and the incident velocity makes an angle [tex]\theta[/tex] 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 [tex]\theta[/tex] come into the setup of the problem?
 
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Anyone have any ideas on this? I just need some advice on how to setup the problem... I am lost on it =/
 

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