Bound state of the delta function potential.

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SUMMARY

The discussion centers on the physical interpretation of bound states with negative energy in the context of the delta function potential. It is established that the delta function potential allows for one bound state with negative energy, which is a common convention in both quantum mechanics and classical physics. The zero point of potential energy is arbitrary, and negative energy indicates that the bound state energy is lower than the chosen zero reference point. The kinetic energy is described as infinite and positive, while the potential energy is infinite and negative, with their difference being well-defined and negative.

PREREQUISITES
  • Understanding of delta function potential in quantum mechanics
  • Familiarity with concepts of bound states and energy levels
  • Knowledge of kinetic and potential energy relationships
  • Basic principles of classical physics regarding energy
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  • Explore the mathematical formulation of the delta function potential in quantum mechanics
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Physicists, students of quantum mechanics, and anyone interested in the theoretical implications of potential energy in bound states.

siddharth5129
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What is the physical meaning to a bound state with negative energy? As I understand it, this is the case with the delta function potential, which admits only one bound state with a negative energy.
If the potential function is identically zero throughout (except at the delta function peak), doesn't this translate to a system with a negative kinetic energy? What am I missing here ?
 
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The zero point of potential energy is arbitrary, so there's no physical significance to a negative energy; negative just means it's less than the energy at whatever we've chosen to be zero. It's a very common, very convenient, convention to choose the zero point so that all the bound states are below it, hence are negative.

This isn't QM, potentials in classical physics work the same way.
 
Kinetic energy is infinite and positive, potential energy is inifinite and negative for the bound state of a delta potential. Only their difference is well defined and negative.
 

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