Energy in quantum mechanics problems

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SUMMARY

In quantum mechanics, the choice of energy values is crucial for solving problems related to scattering, tunneling, and bound states. For bound states, the energy (E) must be less than the potential well, indicating that the particle is trapped. Conversely, for scattering scenarios, the energy must be greater than the potential, allowing the particle to escape while still being influenced by the potential well. This distinction is essential for accurate calculations in quantum mechanics.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with potential wells and bound states
  • Knowledge of scattering theory
  • Basic classical mechanics concepts
NEXT STEPS
  • Study the concept of bound states in quantum mechanics
  • Learn about potential wells and their implications on energy levels
  • Explore scattering theory and its applications in quantum mechanics
  • Investigate tunneling phenomena and its significance in quantum systems
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Students and professionals in physics, particularly those focusing on quantum mechanics, as well as researchers dealing with energy calculations in quantum systems.

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I'm confused about choosing the value for energy in quantum mechanics problems such as in scattering, tunneling, boundstates.. problems because this affects later calculations. Given the potential in some regions, how do I decide energy to be negative or positive, or greater/less than the energy values?
Thank you very much
 
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If you want a bound state then you choose E less than the potential well (think of it classically were a particle is trapped in a well). If you want scattering then you choose E greater than (also think of it classically, where the particle can escape but it will be affected by the well).
 

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