Schrodinger Eq. & Energies: Are Values Always Positive?

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SUMMARY

The discussion centers on the energy values associated with the Schrödinger equation in quantum mechanics. It is established that energy values can indeed be negative, particularly when a particle is in a bound state, where the energy is less than the potential energy required to escape. The existence of a lowest energy eigenvalue is crucial, as it prevents the system from losing an infinite amount of energy.

PREREQUISITES
  • Understanding of the Schrödinger equation
  • Familiarity with quantum mechanics concepts
  • Knowledge of eigenvalues and eigenfunctions
  • Basic principles of bound and unbound states
NEXT STEPS
  • Study the implications of negative energy eigenvalues in quantum systems
  • Learn about the concept of bound states in quantum mechanics
  • Explore the mathematical formulation of the Schrödinger equation
  • Investigate the significance of the lowest energy eigenvalue in quantum systems
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Students and professionals in physics, particularly those specializing in quantum mechanics, as well as researchers interested in the properties of energy states in quantum systems.

oddiseas
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just a question about the energies associted wuth the Schrödinger equation> are the energy values always positive values. I thought that since when the eigenfunctions exist the particle is in a bound state, that the energy should be less than that required to escape a bound state and should be negative.
 
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oddiseas said:
just a question about the energies associted wuth the Schrödinger equation> are the energy values always positive values. I thought that since when the eigenfunctions exist the particle is in a bound state, that the energy should be less than that required to escape a bound state and should be negative.

Yes, the energies can be negative. However, there must exist a lowest energy eigenvalue, otherwise the system could lose an infinite amount of energy.
 

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