For proton and electron of identical energy encounter same potential

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SUMMARY

When a proton and an electron with identical energy encounter the same potential barrier, the probability of transmission varies based on the barrier's height and length, as well as the energy of the particles. For specific barrier parameters, it is possible to find an energy level below the barrier height where one particle achieves a transmission probability of 1, while the other has a probability less than 1. The transmission coefficient T for the case where E < V_0 can be analyzed using the relationship k_1, which is influenced by the particle's mass and the energy difference relative to the barrier height.

PREREQUISITES
  • Quantum mechanics fundamentals
  • Understanding of potential barriers in quantum physics
  • Knowledge of transmission coefficients in quantum tunneling
  • Familiarity with wave functions and their properties
NEXT STEPS
  • Study the transmission coefficient T for quantum tunneling scenarios
  • Explore the concept of wave functions and their role in particle behavior
  • Investigate the implications of mass on quantum tunneling probabilities
  • Review the Wikipedia article on quantum tunneling for deeper insights
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Students and professionals in physics, particularly those focusing on quantum mechanics, as well as researchers exploring particle behavior in potential barriers.

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For proton and electron of identical energy encounter same potential barrier .For which probability of transmission greatest?
 
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That depends on the exact height and length of the barrier as well as the energy of the incident particles. For a given height and length of the barrier you can find an energy less than the height of the barrier for which either particle would have a transmission probability of 1 and the other particle would have something less than 1.

You can see a decent treatment of the problem on Wikipedia. Take a look at the form of the transmission coefficient T for the case [itex]E<V_0[/itex]. If you choose [itex]k_1[/itex] such that [itex]\sin(k_1 a) = 0[/itex] then the transmission coefficient will be 1. [itex]k_1[/itex] depends on the mass of the particle and the difference between the height of the barrier and the energy of the particle.
 

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